code: def test_allowed_transitions(self):
      bio_labels = [
          "O",
          "B-X",
          "I-X",
          "B-Y",
          "I-Y",
      ]  # start tag, end tag
      #              0     1      2      3      4         5          6
      allowed = allowed_transitions("BIO", dict(enumerate(bio_labels)))
  
      # The empty spaces in this matrix indicate disallowed transitions.
      assert set(allowed) == {  # Extra column for end tag.
          (0, 0),
          (0, 1),
          (0, 3),
          (0, 6),
          (1, 0),
          (1, 1),
          (1, 2),
          (1, 3),
          (1, 6),
          (2, 0),
          (2, 1),
          (2, 2),
          (2, 3),
          (2, 6),
          (3, 0),
          (3, 1),
          (3, 3),
          (3, 4),
          (3, 6),
          (4, 0),
          (4, 1),
          (4, 3),
          (4, 4),
          (4, 6),
          (5, 0),
          (5, 1),
          (5, 3),  # Extra row for start tag
      }
  
      bioul_labels = [
          "O",
          "B-X",
          "I-X",
          "L-X",
          "U-X",
          "B-Y",
          "I-Y",
          "L-Y",
          "U-Y",
      ]  # start tag, end tag
      #                0     1      2      3      4      5      6      7      8          9        10
      allowed = allowed_transitions(
          "BIOUL", dict(enumerate(bioul_labels))
      )
  
      # The empty spaces in this matrix indicate disallowed transitions.
      assert set(allowed) == {  # Extra column for end tag.
          (0, 0),
          (0, 1),
          (0, 4),
          (0, 5),
          (0, 8),
          (0, 10),
          (1, 2),
          (1, 3),  # noqa
          (2, 2),
          (2, 3),
          (3, 0),
          (3, 1),
          (3, 4),
          (3, 5),
          (3, 8),
          (3, 10),
          (4, 0),
          (4, 1),
          (4, 4),
          (4, 5),
          (4, 8),
          (4, 10),
          (5, 6),
          (5, 7),
          (6, 6),
          (6, 7),
          (7, 0),
          (7, 1),
          (7, 4),
          (7, 5),
          (7, 8),
          (7, 10),
          (8, 0),
          (8, 1),
          (8, 4),
          (8, 5),
          (8, 8),
          (8, 10),
          # Extra row for start tag.
          (9, 0),
          (9, 1),
          (9, 4),
          (9, 5),
          (9, 8),
      }
  
      iob1_labels = [
          "O",
          "B-X",
          "I-X",
          "B-Y",
          "I-Y",
      ]  # start tag, end tag
      #              0     1      2      3      4         5          6
      allowed = allowed_transitions(
          "IOB1", dict(enumerate(iob1_labels))
      )
  
      # The empty spaces in this matrix indicate disallowed transitions.
      assert set(allowed) == {  # Extra column for end tag.
          (0, 0),
          (0, 2),
          (0, 4),
          (0, 6),
          (1, 0),
          (1, 1),
          (1, 2),
          (1, 4),
          (1, 6),
          (2, 0),
          (2, 1),
          (2, 2),
          (2, 4),
          (2, 6),
          (3, 0),
          (3, 2),
          (3, 3),
          (3, 4),
          (3, 6),
          (4, 0),
          (4, 2),
          (4, 3),
          (4, 4),
          (4, 6),
          (5, 0),
          (5, 2),
          (5, 4),  # Extra row for start tag
      }
      with raises(ConfigurationError):
          allowed_transitions("allennlp", {})
  
      bmes_labels = [
          "B-X",
          "M-X",
          "E-X",
          "S-X",
          "B-Y",
          "M-Y",
          "E-Y",
          "S-Y",
      ]  # start tag, end tag
      #               0      1      2      3      4      5      6      7       8          9
      allowed = allowed_transitions(
          "BMES", dict(enumerate(bmes_labels))
      )
      assert set(allowed) == {
          (0, 1),
          (0, 2),
          (1, 1),
          (1, 2),  # Extra column for end tag.
          (2, 0),
          (2, 3),
          (2, 4),
          (2, 7),
          (2, 9),  # noqa
          (3, 0),
          (3, 3),
          (3, 4),
          (3, 7),
          (3, 9),
          (4, 5),
          (4, 6),
          (5, 5),
          (5, 6),
          (6, 0),
          (6, 3),
          (6, 4),
          (6, 7),
          (6, 9),
          (7, 0),
          (7, 3),
          (7, 4),
          (7, 7),
          (7, 9),
          (8, 0),
          (8, 3),
          (8, 4),
          (8, 7),  # Extra row for start tag
      }
  
imports: import itertools
  import math
  from pytest import approx, raises
  import torch
  from numpy.testing import assert_allclose
  from allennlp.modules import ConditionalRandomField
  from allennlp.modules.conditional_random_field import ConditionalRandomFieldWeightEmission, ConditionalRandomFieldWeightTrans, ConditionalRandomFieldWeightLannoy
  from allennlp.modules.conditional_random_field.conditional_random_field import allowed_transitions
  from allennlp.common.checks import ConfigurationError
  from allennlp.common.testing import AllenNlpTestCase
label_desc: Use image node_id 10 for calling the TestConditionalRandomField obj's underlying member method code with example usage: obj.test_allowed_transitions() without return types