code: def backward(ctx, grad_output):
      if ctx.is_empty:
          bias_grad = (
              None if ctx.bias is None else torch.zeros_like(ctx.bias)
          )
          return (
              torch.zeros_like(ctx.A),
              torch.zeros_like(ctx.B),
              None,
              bias_grad,
              None,
          )
      req_gradA, req_gradB, _, req_gradBias, _ = ctx.needs_input_grad
      CAt, subA, A = ctx.tensors
      SCAt, idx = ctx.tensor_states
      formatB = ctx.formatB
      state = ctx.state
      grad_A = grad_B = grad_bias = None
  
      if req_gradBias:
          # compute grad_bias first before changing grad_output dtype
          grad_bias = grad_output.sum(0, dtype=ctx.dtype_bias)
  
      # Cast grad_output to fp16
      if len(grad_output.shape) == 3:
          grad_output = grad_output.reshape(
              -1, grad_output.shape[-1]
          ).contiguous()
  
      Cgrad, Cgradt, SCgrad, SCgradt, coo_tensor = F.double_quant(
          grad_output.to(torch.float16)
      )
  
      if req_gradB:
          # print('back A shape', A.shape)
          # print('grad output t shape', grad_output.t().shape)
          grad_B = torch.matmul(grad_output.t(), A)
  
      if req_gradA:
          if state.CBt is not None:
              C32grad, Sgrad = F.transform(Cgrad, "col32")
              if state.CxBt is None:
                  state.CxBt, state.SBt = F.transform(
                      state.CBt, to_order=formatB, transpose=True
                  )
              # print('back B shape', state.CxBt.shape)
              # print('back grad shape', C32grad.shape)
              gradA32, SgradA32 = F.igemmlt(
                  C32grad, state.CxBt, Sgrad, state.SBt
              )
              grad_A = (
                  F.mm_dequant(gradA32, SgradA32, SCgrad, state.SCBt)
                  .view(ctx.grad_shape)
                  .to(ctx.dtype_A)
              )
  
          elif state.CB is not None:
              CB = state.CB.to(ctx.dtype_A, copy=True).mul_(
                  state.SCB.unsqueeze(1).mul(1.0 / 127.0)
              )
              grad_A = (
                  torch.matmul(grad_output, CB)
                  .view(ctx.grad_shape)
                  .to(ctx.dtype_A)
              )
          else:
              raise Exception(
                  "State must contain either CBt or CB matrix for backward"
              )
  
      return grad_A, grad_B, None, grad_bias, None
  
imports: import operator
  import warnings
  from dataclasses import dataclass
  from functools import reduce
  import torch
  import bitsandbytes.functional
  from bitsandbytes.autograd._functions import MatmulLtState, GlobalOutlierPooler
label_desc: Use image node_id 2 for calling the SwitchBackBnb obj's underlying member method code with example usage: obj.backward(ctx, grad_output) and returns: grad_A,  grad_B,  None,  grad_bias,  None, torch,  torch,  None,  bias_grad,  None