code: def test_ard_separate_batch(self):
      a = torch.tensor(
          [[[1, 2, 3], [2, 4, 3]], [[2, -1, 2], [2, -1, 0]]],
          dtype=torch.float,
      )
      b = torch.tensor(
          [[[1, 4, 3]], [[2, -1, 0]]], dtype=torch.float
      ).repeat(1, 2, 1)
      lengthscales = torch.tensor(
          [[[1, 2, 1]], [[2, 1, 0.5]]], dtype=torch.float
      )
  
      kernel = MaternKernel(
          nu=2.5, batch_shape=torch.Size([2]), ard_num_dims=3
      )
      kernel.initialize(lengthscale=lengthscales)
      kernel.eval()
  
      dist = torch.tensor(
          [[[1, 1], [1, 1]], [[4, 4], [0, 0]]], dtype=torch.float
      ).mul_(math.sqrt(5))
      actual = (dist**2 / 3 + dist + 1).mul(torch.exp(-dist))
      res = kernel(a, b).to_dense()
      self.assertLess(torch.norm(res - actual), 1e-3)
  
      # diag
      res = kernel(a, b).diagonal(dim1=-1, dim2=-2)
      actual = torch.cat(
          [
              actual[i].diagonal(dim1=-1, dim2=-2).unsqueeze(0)
              for i in range(actual.size(0))
          ]
      )
      self.assertLess(torch.norm(res - actual), 1e-5)
  
      # batch_dims
      dist = torch.tensor(
          [
              [[[0.0, 0.0], [1.0, 1.0]], [[0.0, 0.0], [0.0, 0.0]]],
              [[[1.0, 1.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]],
              [[[0.0, 0.0], [0.0, 0.0]], [[4.0, 4.0], [0.0, 0.0]]],
          ]
      )
  
      dist.mul_(math.sqrt(5))
      dist = dist.view(3, 2, 2, 2).transpose(0, 1)
      actual = (dist**2 / 3 + dist + 1).mul(torch.exp(-dist))
      res = kernel(a, b, last_dim_is_batch=True).to_dense()
      self.assertLess(torch.norm(res - actual), 1e-5)
  
      # batch_dims + diag
      res = kernel(a, b, last_dim_is_batch=True).diagonal(
          dim1=-1, dim2=-2
      )
      actual = actual.diagonal(dim1=-2, dim2=-1)
      self.assertLess(torch.norm(res - actual), 1e-5)
  
imports: import math
  import pickle
  import unittest
  import torch
  from gpytorch.kernels import MaternKernel
  from gpytorch.priors import NormalPrior
  from gpytorch.test.base_kernel_test_case import BaseKernelTestCase
label_desc: Use image node_id 8 for calling the TestMaternKernel obj's underlying member method code with example usage: obj.test_ard_separate_batch() without return types