code: def partitions(s, include_singles=True):
      """Partitions a sequence into all groupings of pairs and singles of elements.
  
      Args:
          s (sequence): the sequence to partition
          include_singles (bool): if False, only partitions into pairs
              is returned.
  
      Returns:
          tuple: returns a nested tuple, containing all partitions of the sequence.
      """
      # pylint: disable=too-many-branches
      if len(s) == 2:
          if include_singles:
              yield (s[0],), (s[1],)
  
          yield (tuple(s),)
      else:
          # pull off a single item and partition the rest
          if include_singles:
              if len(s) > 1:
                  item_partition = (s[0],)
                  rest = s[1:]
                  rest_partitions = partitions(rest, include_singles)
                  for p in rest_partitions:
                      yield ((item_partition),) + p
              else:
                  yield (tuple(s),)
  
          # pull off a pair of items and partition the rest
          for idx1 in range(1, len(s)):
              item_partition = (s[0], s[idx1])
              rest = s[1:idx1] + s[idx1 + 1 :]
              rest_partitions = partitions(rest, include_singles)
              for p in rest_partitions:
                  yield ((item_partition),) + p
  
imports: import math
  import cmath
  import numpy
  from scipy.special import factorial
  import pennylane
  from pennylane.ops import Identity
  from pennylane import Device
  from .._version import __version__
label_desc: Use image node_id 1 for calling a global function with example usage: partitions(s, include_singles) without return types