code: def test_computes_downsampling_function_batch(self):
      a = torch.tensor([[0.1, 0.2], [0.3, 0.4], [0.5, 0.5]]).view(
          3, 2, 1
      )
      b = torch.tensor([[0.5, 0.6], [0.7, 0.8], [0.6, 0.6]]).view(
          3, 2, 1
      )
      power = 1
      offset = 1
  
      kernel = DownsamplingKernel(batch_shape=torch.Size([3]))
      kernel.initialize(power=power, offset=offset)
      kernel.eval()
      res = kernel(a, b).to_dense()
  
      actual = torch.zeros(3, 2, 2)
  
      diff = torch.tensor([[0.45, 0.36], [0.4, 0.32]])
      actual[0, :, :] = offset + diff.pow(1 + power)
  
      diff = torch.tensor([[0.21, 0.14], [0.18, 0.12]])
      actual[1, :, :] = offset + diff.pow(1 + power)
  
      diff = torch.tensor([[0.2, 0.2], [0.2, 0.2]])
      actual[2, :, :] = offset + diff.pow(1 + power)
      self.assertLess(torch.linalg.norm(res - actual), 1e-5)
  
imports: import torch
  from botorch.models.kernels.downsampling import DownsamplingKernel
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.priors.torch_priors import GammaPrior, NormalPrior
  from gpytorch.test.base_kernel_test_case import BaseKernelTestCase
label_desc: Use image node_id 10 for calling the TestDownsamplingKernel obj's underlying member method code with example usage: obj.test_computes_downsampling_function_batch() without return types