new_contents: #!/usr/bin/env python3
  import torch
  import math
  from pykeops.torch import LazyTensor as KEOLazyTensor
  from ..kernel import Kernel
  from gpytorch.lazy import KeOpsLazyTensor
  
  
  class MaternKernel(Kernel):
      def __init__(self, nu=2.5, **kwargs):
          if nu not in {0.5, 1.5, 2.5}:
              raise RuntimeError("nu expected to be 0.5, 1.5, or 2.5")
          super(MaternKernel, self).__init__(has_lengthscale=True, **kwargs)
          self.nu = nu
  
      def covar_func(self, x1, x2, diag=False):
          # TODO: x1 / x2 size checks are a work around for a very minor bug in KeOps.
          # This bug is fixed on KeOps master, and we'll remove that part of the check
          # when they cut a new release.
          if diag or x1.size(-2) == 1 or x2.size(-2) == 1:
              distance = self.covar_dist(x1, x2, diag=diag)
              exp_component = torch.exp(-math.sqrt(self.nu * 2) * distance)
  
              if self.nu == 0.5:
                  constant_component = 1
              elif self.nu == 1.5:
                  constant_component = (math.sqrt(3) * distance).add(1)
              elif self.nu == 2.5:
                  constant_component = (math.sqrt(5) * distance).add(1).add(5.0 / 3.0 * distance ** 2)
              return constant_component * exp_component
          else:
              with torch.autograd.enable_grad():
                  x1_ = KEOLazyTensor(x1[:, None, :])
                  x2_ = KEOLazyTensor(x2[None, :, :])
  
                  distance = ((x1_ - x2_) ** 2).sum(-1).sqrt()
                  exp_component = (-math.sqrt(self.nu * 2) * distance).exp()
  
                  if self.nu == 0.5:
                      constant_component = 1
                  elif self.nu == 1.5:
                      constant_component = (math.sqrt(3) * distance) + 1
                  elif self.nu == 2.5:
                      constant_component = (math.sqrt(5) * distance) + (1 + 5.0 / 3.0 * distance ** 2)
  
                  return constant_component * exp_component
  
      def forward(self, x1, x2, diag=False, **params):
          mean = x1.contiguous().view(-1, x1.size(-1)).mean(0)[(None,) * (x1.dim() - 1)]
  
          x1_ = (x1 - mean).div(self.lengthscale)
          x2_ = (x2 - mean).div(self.lengthscale)
  
          if diag:
              return self.covar_func(x1_, x2_, diag=True)
  
          covar_func = lambda x1, x2, diag=False: self.covar_func(x1, x2, diag)
          return KeOpsLazyTensor(x1_, x2_, covar_func)
  
subject: Implement KeOps MaternKernel