code: def test_sort_index_nan_multiindex(self):
      # GH#14784
      # incorrect sorting w.r.t. nans
      tuples = [[12, 13], [np.nan, np.nan], [np.nan, 3], [1, 2]]
      mi = MultiIndex.from_tuples(tuples)
  
      df = DataFrame(
          np.arange(16).reshape(4, 4), index=mi, columns=list("ABCD")
      )
      s = Series(np.arange(4), index=mi)
  
      df2 = DataFrame(
          {
              "date": pd.DatetimeIndex(
                  [
                      "20121002",
                      "20121007",
                      "20130130",
                      "20130202",
                      "20130305",
                      "20121002",
                      "20121207",
                      "20130130",
                      "20130202",
                      "20130305",
                      "20130202",
                      "20130305",
                  ]
              ),
              "user_id": [1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5, 5],
              "whole_cost": [
                  1790,
                  np.nan,
                  280,
                  259,
                  np.nan,
                  623,
                  90,
                  312,
                  np.nan,
                  301,
                  359,
                  801,
              ],
              "cost": [12, 15, 10, 24, 39, 1, 0, np.nan, 45, 34, 1, 12],
          }
      ).set_index(["date", "user_id"])
  
      # sorting frame, default nan position is last
      result = df.sort_index()
      expected = df.iloc[[3, 0, 2, 1], :]
      tm.assert_frame_equal(result, expected)
  
      # sorting frame, nan position last
      result = df.sort_index(na_position="last")
      expected = df.iloc[[3, 0, 2, 1], :]
      tm.assert_frame_equal(result, expected)
  
      # sorting frame, nan position first
      result = df.sort_index(na_position="first")
      expected = df.iloc[[1, 2, 3, 0], :]
      tm.assert_frame_equal(result, expected)
  
      # sorting frame with removed rows
      result = df2.dropna().sort_index()
      expected = df2.sort_index().dropna()
      tm.assert_frame_equal(result, expected)
  
      # sorting series, default nan position is last
      result = s.sort_index()
      expected = s.iloc[[3, 0, 2, 1]]
      tm.assert_series_equal(result, expected)
  
      # sorting series, nan position last
      result = s.sort_index(na_position="last")
      expected = s.iloc[[3, 0, 2, 1]]
      tm.assert_series_equal(result, expected)
  
      # sorting series, nan position first
      result = s.sort_index(na_position="first")
      expected = s.iloc[[1, 2, 3, 0]]
      tm.assert_series_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 4 for calling the TestDataFrameSortIndex obj's underlying member method code with example usage: obj.test_sort_index_nan_multiindex() without return types