code: def test_sort_index_and_reconstruction(self):
      # GH#15622
      # lexsortedness should be identical
      # across MultiIndex construction methods
  
      df = DataFrame([[1, 1], [2, 2]], index=list("ab"))
      expected = DataFrame(
          [[1, 1], [2, 2], [1, 1], [2, 2]],
          index=MultiIndex.from_tuples(
              [(0.5, "a"), (0.5, "b"), (0.8, "a"), (0.8, "b")]
          ),
      )
      assert expected.index._is_lexsorted()
  
      result = DataFrame(
          [[1, 1], [2, 2], [1, 1], [2, 2]],
          index=MultiIndex.from_product([[0.5, 0.8], list("ab")]),
      )
      result = result.sort_index()
      assert result.index.is_monotonic_increasing
  
      tm.assert_frame_equal(result, expected)
  
      result = DataFrame(
          [[1, 1], [2, 2], [1, 1], [2, 2]],
          index=MultiIndex(
              levels=[[0.5, 0.8], ["a", "b"]],
              codes=[[0, 0, 1, 1], [0, 1, 0, 1]],
          ),
      )
      result = result.sort_index()
      assert result.index._is_lexsorted()
  
      tm.assert_frame_equal(result, expected)
  
      concatted = pd.concat([df, df], keys=[0.8, 0.5])
      result = concatted.sort_index()
  
      assert result.index.is_monotonic_increasing
  
      tm.assert_frame_equal(result, expected)
  
      # GH#14015
      df = DataFrame(
          [[1, 2], [6, 7]],
          columns=MultiIndex.from_tuples(
              [(0, "20160811 12:00:00"), (0, "20160809 12:00:00")],
              names=["l1", "Date"],
          ),
      )
  
      df.columns = df.columns.set_levels(
          pd.to_datetime(df.columns.levels[1]), level=1
      )
      assert not df.columns.is_monotonic_increasing
      result = df.sort_index(axis=1)
      assert result.columns.is_monotonic_increasing
      result = df.sort_index(axis=1, level=1)
      assert result.columns.is_monotonic_increasing
  
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 18 for calling the TestDataFrameSortIndex obj's underlying member method code with example usage: obj.test_sort_index_and_reconstruction() without return types