code: def test_bisect(self):
      def f(x):
          return 1 + x
  
      for dtype, batch_shape in itertools.product(
          (torch.float, torch.double), ([5], [6, 5, 2])
      ):
          tkwargs = {"device": self.device, "dtype": dtype}
          bounds = torch.stack(
              (
                  torch.zeros(batch_shape, **tkwargs),
                  torch.ones(batch_shape, **tkwargs),
              )
          )
          for target, tol in itertools.product(
              [1.01, 1.5, 1.99], [1e-3, 1e-6]
          ):
              x = batched_bisect(
                  f=f, target=target, bounds=bounds, tol=tol
              )
              self.assertAllClose(
                  f(x),
                  torch.full(batch_shape, target, **tkwargs),
                  atol=tol,
              )
          # Do one step and make sure we didn't converge in this case
          x = batched_bisect(
              f=f, target=1.71, bounds=bounds, max_steps=1
          )
          self.assertAllClose(
              x, torch.full(batch_shape, 0.75, **tkwargs), atol=tol
          )
          # Target outside the bounds should raise
          with self.assertRaisesRegex(
              ValueError,
              "The target is not contained in the interval specified by the bounds",
          ):
              batched_bisect(f=f, target=2.1, bounds=bounds)
          # Test analytic solution when there is only one MCMC sample
          mean = torch.randn(1, 5, **tkwargs)
          variance = torch.rand(1, 5, **tkwargs)
          covar = torch.diag_embed(variance)
          mvn = MultivariateNormal(mean, to_linear_operator(covar))
          posterior = GaussianMixturePosterior(distribution=mvn)
          dist = torch.distributions.Normal(
              loc=mean.unsqueeze(-1),
              scale=variance.unsqueeze(-1).sqrt(),
          )
          for q in [0.1, 0.5, 0.9]:
              x = posterior.quantile(value=torch.tensor(q))
              self.assertAllClose(
                  dist.cdf(x),
                  q * torch.ones(1, 5, 1, **tkwargs),
                  atol=1e-4,
              )
  
imports: import itertools
  from unittest import mock
  from unittest.mock import patch
  import pyro
  import torch
  from botorch import fit_fully_bayesian_model_nuts, utils
  from botorch.acquisition.analytic import ExpectedImprovement, PosteriorMean, ProbabilityOfImprovement, UpperConfidenceBound
  from botorch.acquisition.logei import qLogExpectedImprovement, qLogNoisyExpectedImprovement
  from botorch.acquisition.monte_carlo import qExpectedImprovement, qNoisyExpectedImprovement, qProbabilityOfImprovement, qSimpleRegret, qUpperConfidenceBound
  from botorch.acquisition.multi_objective import prune_inferior_points_multi_objective, qExpectedHypervolumeImprovement, qNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.multi_objective.logei import qLogExpectedHypervolumeImprovement, qLogNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.utils import prune_inferior_points
  from botorch.models import ModelList, ModelListGP
  from botorch.models.deterministic import GenericDeterministicModel
  from botorch.models.fully_bayesian import MCMC_DIM, MIN_INFERRED_NOISE_LEVEL, PyroModel, SaasFullyBayesianSingleTaskGP, SaasPyroModel
  from botorch.models.transforms import Normalize, Standardize
  from botorch.posteriors.fully_bayesian import batched_bisect, GaussianMixturePosterior
  from botorch.sampling.get_sampler import get_sampler
  from botorch.utils.datasets import SupervisedDataset
  from botorch.utils.multi_objective.box_decompositions.non_dominated import NondominatedPartitioning
  from botorch.utils.safe_math import logmeanexp
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.kernels import MaternKernel, ScaleKernel
  from gpytorch.likelihoods import FixedNoiseGaussianLikelihood, GaussianLikelihood
  from gpytorch.means import ConstantMean
  from linear_operator.operators import to_linear_operator
  from pyro.ops.integrator import _EXCEPTION_HANDLERS, potential_grad, register_exception_handler
label_desc: Use image node_id 13 for calling the TestFullyBayesianSingleTaskGP obj's underlying member method code with example usage: obj.test_bisect() and returns: unknown