code: def test_monotonic(self, closed):
      # increasing non-overlapping
      idx = IntervalIndex.from_tuples(
          [(0, 1), (2, 3), (4, 5)], closed=closed
      )
      assert idx.is_monotonic_increasing is True
      assert idx._is_strictly_monotonic_increasing is True
      assert idx.is_monotonic_decreasing is False
      assert idx._is_strictly_monotonic_decreasing is False
  
      # decreasing non-overlapping
      idx = IntervalIndex.from_tuples(
          [(4, 5), (2, 3), (1, 2)], closed=closed
      )
      assert idx.is_monotonic_increasing is False
      assert idx._is_strictly_monotonic_increasing is False
      assert idx.is_monotonic_decreasing is True
      assert idx._is_strictly_monotonic_decreasing is True
  
      # unordered non-overlapping
      idx = IntervalIndex.from_tuples(
          [(0, 1), (4, 5), (2, 3)], closed=closed
      )
      assert idx.is_monotonic_increasing is False
      assert idx._is_strictly_monotonic_increasing is False
      assert idx.is_monotonic_decreasing is False
      assert idx._is_strictly_monotonic_decreasing is False
  
      # increasing overlapping
      idx = IntervalIndex.from_tuples(
          [(0, 2), (0.5, 2.5), (1, 3)], closed=closed
      )
      assert idx.is_monotonic_increasing is True
      assert idx._is_strictly_monotonic_increasing is True
      assert idx.is_monotonic_decreasing is False
      assert idx._is_strictly_monotonic_decreasing is False
  
      # decreasing overlapping
      idx = IntervalIndex.from_tuples(
          [(1, 3), (0.5, 2.5), (0, 2)], closed=closed
      )
      assert idx.is_monotonic_increasing is False
      assert idx._is_strictly_monotonic_increasing is False
      assert idx.is_monotonic_decreasing is True
      assert idx._is_strictly_monotonic_decreasing is True
  
      # unordered overlapping
      idx = IntervalIndex.from_tuples(
          [(0.5, 2.5), (0, 2), (1, 3)], closed=closed
      )
      assert idx.is_monotonic_increasing is False
      assert idx._is_strictly_monotonic_increasing is False
      assert idx.is_monotonic_decreasing is False
      assert idx._is_strictly_monotonic_decreasing is False
  
      # increasing overlapping shared endpoints
      idx = IntervalIndex.from_tuples(
          [(1, 2), (1, 3), (2, 3)], closed=closed
      )
      assert idx.is_monotonic_increasing is True
      assert idx._is_strictly_monotonic_increasing is True
      assert idx.is_monotonic_decreasing is False
      assert idx._is_strictly_monotonic_decreasing is False
  
      # decreasing overlapping shared endpoints
      idx = IntervalIndex.from_tuples(
          [(2, 3), (1, 3), (1, 2)], closed=closed
      )
      assert idx.is_monotonic_increasing is False
      assert idx._is_strictly_monotonic_increasing is False
      assert idx.is_monotonic_decreasing is True
      assert idx._is_strictly_monotonic_decreasing is True
  
      # stationary
      idx = IntervalIndex.from_tuples([(0, 1), (0, 1)], closed=closed)
      assert idx.is_monotonic_increasing is True
      assert idx._is_strictly_monotonic_increasing is False
      assert idx.is_monotonic_decreasing is True
      assert idx._is_strictly_monotonic_decreasing is False
  
      # empty
      idx = IntervalIndex([], closed=closed)
      assert idx.is_monotonic_increasing is True
      assert idx._is_strictly_monotonic_increasing is True
      assert idx.is_monotonic_decreasing is True
      assert idx._is_strictly_monotonic_decreasing is True
  
imports: from itertools import permutations
  import re
  import numpy
  import pytest
  import pandas
  from pandas import Index, Interval, IntervalIndex, Timedelta, Timestamp, date_range, interval_range, isna, notna, timedelta_range
  import pandas._testing
  import pandas.core.common
label_desc: Use image node_id 11 for calling the TestIntervalIndex obj's underlying member method code with example usage: obj.test_monotonic(closed) without return types