code: def flatten_fun_for_sparse_ad(
      fun, argnums: int | tuple[int], args: tuple[Any]
  ):
      argnums_tup = _ensure_index_tuple(argnums)
      assert all(0 <= argnum < len(args) for argnum in argnums_tup)
  
      # We do a two-step flattening to figure out how argnums maps to args_flat.
      # First, flatten arguments to a list containing sparse and dense objects.
      args_flat1, tree1 = tree_util.tree_flatten(
          args, is_leaf=is_sparse
      )
      *leaf_argnums1, end = split_list(
          range(tree1.num_leaves),
          [child.num_leaves for child in tree1.children()],
      )
      assert not end
      argnums_flat1 = list(
          itertools.chain.from_iterable(
              nums
              for i, nums in enumerate(leaf_argnums1)
              if i in argnums_tup
          )
      )
  
      # Next, fully flatten to a list of dense buffers.
      args_flat, tree2 = tree_util.tree_flatten(args_flat1)
      *leaf_argnums2, end = split_list(
          range(tree2.num_leaves),
          [child.num_leaves for child in tree2.children()],
      )
      assert not end
      # For sparse args, we only mark the first buffer (the data) for differentiation.
      leaf_argnums2 = [
          nums[:1] if is_sparse(arg) else nums
          for arg, nums in safe_zip(args_flat1, leaf_argnums2)
      ]
      argnums_flat = tuple(
          itertools.chain.from_iterable(
              nums
              for i, nums in enumerate(leaf_argnums2)
              if i in argnums_flat1
          )
      )
  
      def fun_flat(*args_flat, **kwargs):
          args = tree_util.tree_unflatten(
              tree1, tree_util.tree_unflatten(tree2, args_flat)
          )
          return fun(*args, **kwargs)
  
      def reconstruct(i, grad_out):
          bufs, tree = tree_util.tree_flatten(args_flat1[i])
          f_recons = lambda g: tree_util.tree_unflatten(
              tree, [g, *bufs[1:]]
          )
          for _ in range(grad_out.ndim - bufs[0].ndim):
              f_recons = jax.vmap(f_recons)
          return f_recons(grad_out)
  
      def postprocess_gradients(grads_out):
          out = [
              reconstruct(*args)
              for args in safe_zip(argnums_flat1, grads_out)
          ]
          return out[0] if isinstance(argnums, int) else out
  
      return fun_flat, argnums_flat, args_flat, postprocess_gradients
  
file_path: jax/jax/experimental/sparse/ad.py
imports: from __future__ import annotations
  from collections.abc import Sequence
  import itertools
  from typing import Any, Callable, Union
  import jax
  from jax._src import core
  from jax import tree_util
  from jax._src.api_util import _ensure_index, _ensure_index_tuple
  from jax.util import safe_zip
  from jax._src.util import split_list, wraps
  from jax._src.traceback_util import api_boundary
  from jax.experimental.sparse._base import JAXSparse
label_desc: Use image node_id 1 for calling a global function with example usage: flatten_fun_for_sparse_ad(fun, argnums, args) and returns: fun_flat,  argnums_flat,  args_flat,  postprocess_gradients, fun, f_recons, unknown