code: def backward(ctx, D_grad, U_grad):
      A_grad = B_grad = None
      grads = [None] * 14
  
      A, B, D, U = ctx.saved_tensors
      largest = ctx.largest
  
      # lobpcg.backward has some limitations. Checks for unsupported input
      if A.is_sparse or (
          B is not None and B.is_sparse and ctx.needs_input_grad[2]
      ):
          raise ValueError(
              "lobpcg.backward does not support sparse input yet."
              "Note that lobpcg.forward does though."
          )
      if (
          A.dtype in (torch.complex64, torch.complex128)
          or B is not None
          and B.dtype in (torch.complex64, torch.complex128)
      ):
          raise ValueError(
              "lobpcg.backward does not support complex input yet."
              "Note that lobpcg.forward does though."
          )
      if B is not None:
          raise ValueError(
              "lobpcg.backward does not support backward with B != I yet."
          )
  
      if largest is None:
          largest = True
  
      # symeig backward
      if B is None:
          A_grad = _symeig_backward(D_grad, U_grad, A, D, U, largest)
  
      # A has index 0
      grads[0] = A_grad
      # B has index 2
      grads[2] = B_grad
      return tuple(grads)
  
imports: from typing import Dict, Optional, Tuple
  import torch
  from torch import Tensor
  from .None import _linalg_utils
  from .overrides import handle_torch_function, has_torch_function
label_desc: Use image node_id 2 for calling the LOBPCGAutogradFunction obj's underlying member method code with example usage: obj.backward(ctx, D_grad, U_grad) and returns: tuple