code: def forward(ctx, x1, x2, lengthscale, nu, dist_func):
      if any(ctx.needs_input_grad[:2]):
          raise RuntimeError(
              "MaternCovariance cannot compute gradients with "
              "respect to x1 and x2"
          )
      if lengthscale.size(-1) > 1:
          raise ValueError(
              "MaternCovariance cannot handle multiple lengthscales"
          )
      # Subtract mean for numerical stability. Won't affect computations
      # because covariance matrix is stationary.
      needs_grad = any(ctx.needs_input_grad)
      mean = x1.mean(dim=-2, keepdim=True)
      x1_ = (x1 - mean).div(lengthscale)
      x2_ = (x2 - mean).div(lengthscale)
      scaled_unitless_dist = dist_func(x1_, x2_).mul_(math.sqrt(2 * nu))
      if nu == 0.5:
          # 1 kernel sized Tensor if no grad else 2
          scaled_unitless_dist_ = (
              scaled_unitless_dist.clone()
              if needs_grad
              else scaled_unitless_dist
          )
          exp_component = scaled_unitless_dist_.neg_().exp_()
          covar_mat = exp_component
          if needs_grad:
              d_output_d_input = scaled_unitless_dist.div_(
                  lengthscale
              ).mul_(exp_component)
      elif nu == 1.5:
          # 2 kernel sized Tensors if no grad else 3
          if needs_grad:
              scaled_unitless_dist_ = scaled_unitless_dist.clone()
          linear_term = scaled_unitless_dist.clone().add_(1)
          exp_component = scaled_unitless_dist.neg_().exp_()
          covar_mat = linear_term.mul_(exp_component)
          if needs_grad:
              d_output_d_input = (
                  scaled_unitless_dist_.pow_(2)
                  .div_(lengthscale)
                  .mul_(exp_component)
              )
      elif nu == 2.5:
          # 3 kernel sized Tensors if no grad else 4
          linear_term = scaled_unitless_dist.clone().add_(1)
          quadratic_term = scaled_unitless_dist.clone().pow_(2).div_(3)
          exp_component = scaled_unitless_dist.neg_().exp_()
          if needs_grad:
              covar_mat = (linear_term + quadratic_term).mul_(
                  exp_component
              )
              d_output_d_input = (
                  linear_term.mul_(quadratic_term)
                  .mul_(exp_component)
                  .div_(lengthscale)
              )
          else:
              covar_mat = exp_component.mul_(
                  linear_term.add_(quadratic_term)
              )
      if needs_grad:
          ctx.save_for_backward(d_output_d_input)
      return covar_mat
  
imports: import math
  import torch
label_desc: Use image node_id 1 for calling the MaternCovariance obj's underlying member method code with example usage: obj.forward(ctx, x1, x2, lengthscale, nu, dist_func) and returns: covar_mat