code: def test_compute_linear_truncated_kernel_with_batch(self):
      x1 = torch.tensor(
          [
              [[1.0, 0.1, 0.2], [3.0, 0.3, 0.4]],
              [[5.0, 0.5, 0.6], [7.0, 0.7, 0.8]],
          ]
      )
      x2 = torch.tensor(
          [
              [[2.0, 0.8, 0.7], [4.0, 0.6, 0.5]],
              [[6.0, 0.4, 0.3], [8.0, 0.2, 0.1]],
          ]
      )
      t_1 = torch.tensor(
          [
              [[0.2736, 0.4400], [0.2304, 0.3600]],
              [[0.3304, 0.3816], [0.1736, 0.1944]],
          ]
      )
      batch_shape = torch.Size([2])
      for nu, fidelity_dims in itertools.product(
          {0.5, 1.5, 2.5}, ([2], [1, 2])
      ):
          kernel = LinearTruncatedFidelityKernel(
              fidelity_dims=fidelity_dims,
              dimension=3,
              nu=nu,
              batch_shape=batch_shape,
          )
          kernel.power = 1
          if len(fidelity_dims) > 1:
              active_dimsM = [0]
              t_2 = torch.tensor(
                  [
                      [[0.0527, 0.1670], [0.0383, 0.1159]],
                      [[0.1159, 0.1670], [0.0383, 0.0527]],
                  ]
              )
              t_3 = torch.tensor(
                  [
                      [[0.1944, 0.3816], [0.1736, 0.3304]],
                      [[0.3600, 0.4400], [0.2304, 0.2736]],
                  ]
              )
              t = 1 + t_1 + t_2 + t_3
          else:
              active_dimsM = [0, 1]
              t = 1 + t_1
  
          matern_ker = MaternKernel(
              nu=nu, active_dims=active_dimsM, batch_shape=batch_shape
          )
          matern_term = matern_ker(x1, x2).to_dense()
          actual = t * matern_term
          res = kernel(x1, x2).to_dense()
          self.assertLess(torch.linalg.norm(res - actual), 1e-4)
          # test diagonal mode
          res_diag = kernel(x1, x2, diag=True)
          self.assertLess(
              torch.linalg.norm(
                  res_diag - torch.diagonal(actual, dim1=-1, dim2=-2)
              ),
              1e-4,
          )
      # make sure that we error out if last_dim_is_batch=True
      with self.assertRaises(NotImplementedError):
          kernel(x1, x2, diag=True, last_dim_is_batch=True)
  
imports: import itertools
  import torch
  from botorch.exceptions import UnsupportedError
  from botorch.models.kernels.linear_truncated_fidelity import LinearTruncatedFidelityKernel
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.kernels.matern_kernel import MaternKernel
  from gpytorch.kernels.rbf_kernel import RBFKernel
  from gpytorch.priors.torch_priors import GammaPrior, NormalPrior
  from gpytorch.test.base_kernel_test_case import BaseKernelTestCase
label_desc: Use image node_id 6 for calling the TestLinearTruncatedFidelityKernel obj's underlying member method code with example usage: obj.test_compute_linear_truncated_kernel_with_batch() without return types