code: def test_sort_multi_index_key(self):
      # GH 25775, testing that sorting by index works with a multi-index.
      df = DataFrame(
          {
              "a": [3, 1, 2],
              "b": [0, 0, 0],
              "c": [0, 1, 2],
              "d": list("abc"),
          }
      ).set_index(list("abc"))
  
      result = df.sort_index(level=list("ac"), key=lambda x: x)
  
      expected = DataFrame(
          {
              "a": [1, 2, 3],
              "b": [0, 0, 0],
              "c": [1, 2, 0],
              "d": list("bca"),
          }
      ).set_index(list("abc"))
      tm.assert_frame_equal(result, expected)
  
      result = df.sort_index(level=list("ac"), key=lambda x: -x)
      expected = DataFrame(
          {
              "a": [3, 2, 1],
              "b": [0, 0, 0],
              "c": [0, 2, 1],
              "d": list("acb"),
          }
      ).set_index(list("abc"))
  
      tm.assert_frame_equal(result, expected)
  
imports: import numpy
  import pytest
  import pandas
  from pandas import CategoricalDtype, CategoricalIndex, DataFrame, IntervalIndex, MultiIndex, RangeIndex, Series, Timestamp
  import pandas._testing
label_desc: Use image node_id 1 for calling the TestDataFrameSortIndexKey obj's underlying member method code with example usage: obj.test_sort_multi_index_key() without return types