code: def group_observables(
      observables, coefficients=None, grouping_type="qwc", method="rlf"
  ):
      """Partitions a list of observables (Pauli operations and tensor products thereof) into
      groupings according to a binary relation (qubit-wise commuting, fully-commuting, or
      anticommuting).
  
      Partitions are found by 1) mapping the list of observables to a graph where vertices represent
      observables and edges encode the binary relation, then 2) solving minimum clique cover for the
      graph using graph-colouring heuristic algorithms.
  
      Args:
          observables (list[Observable]): a list of Pauli word ``Observable`` instances (Pauli
              operation instances and :class:`~.Tensor` instances thereof)
          coefficients (tensor_like): A tensor or list of coefficients. If not specified,
              output ``partitioned_coeffs`` is not returned.
          grouping_type (str): The type of binary relation between Pauli words.
              Can be ``'qwc'``, ``'commuting'``, or ``'anticommuting'``.
          method (str): the graph coloring heuristic to use in solving minimum clique cover, which
              can be ``'lf'`` (Largest First) or ``'rlf'`` (Recursive Largest First)
  
      Returns:
         tuple:
  
             * list[list[Observable]]: A list of the obtained groupings. Each grouping
               is itself a list of Pauli word ``Observable`` instances.
             * list[tensor_like]: A list of coefficient groupings. Each coefficient
               grouping is itself a tensor or list of the grouping's corresponding coefficients. This is only
               returned if coefficients are specified.
  
      Raises:
          IndexError: if the input list of coefficients is not of the same length as the input list
              of Pauli words
  
      **Example**
  
      >>> obs = [qml.PauliY(0), qml.PauliX(0) @ qml.PauliX(1), qml.PauliZ(1)]
      >>> coeffs = [1.43, 4.21, 0.97]
      >>> obs_groupings, coeffs_groupings = group_observables(obs, coeffs, 'anticommuting', 'lf')
      >>> obs_groupings
      [[PauliZ(wires=[1]), PauliX(wires=[0]) @ PauliX(wires=[1])],
       [PauliY(wires=[0])]]
      >>> coeffs_groupings
      [[0.97, 4.21], [1.43]]
      """
  
      if coefficients is not None:
          if qml.math.shape(coefficients)[0] != len(observables):
              raise IndexError(
                  "The coefficients list must be the same length as the observables list."
              )
  
      pauli_grouping = PauliGroupingStrategy(
          observables,
          grouping_type=grouping_type,
          graph_colourer=method,
      )
      partitioned_paulis = pauli_grouping.colour_pauli_graph()
  
      if coefficients is None:
          return partitioned_paulis
  
      partitioned_coeffs = [
          qml.math.cast_like([0] * len(g), coefficients)
          for g in partitioned_paulis
      ]
  
      observables = copy(observables)
      # we cannot delete elements from the coefficients tensor, so we
      # use a proxy list memorising the indices for this logic
      coeff_indices = list(range(qml.math.shape(coefficients)[0]))
      for i, partition in enumerate(
          partitioned_paulis
      ):  # pylint:disable=too-many-nested-blocks
          indices = []
          for pauli_word in partition:
              # find index of this pauli word in remaining original observables,
              for observable in observables:
                  if are_identical_pauli_words(pauli_word, observable):
                      for ind, obs in enumerate(observables):
                          if obs is not observable:
                              continue
                          indices.append(coeff_indices[ind])
                          observables.pop(ind)
                          coeff_indices.pop(ind)
                          break
                      break
  
          # add a tensor of coefficients to the grouped coefficients
          partitioned_coeffs[i] = qml.math.take(
              coefficients, indices, axis=0
          )
  
      # make sure the output is of the same format as the input
      # for these two frequent cases
      if isinstance(coefficients, list):
          partitioned_coeffs = [list(p) for p in partitioned_coeffs]
  
      return partitioned_paulis, partitioned_coeffs
  
file_path: pennylane/pennylane/pauli/grouping/group_observables.py
imports: from copy import copy
  import numpy
  import pennylane
  from pennylane.pauli.utils import are_identical_pauli_words, binary_to_pauli, observables_to_binary_matrix, qwc_complement_adj_matrix
  from pennylane.wires import Wires
  from .graph_colouring import largest_first, recursive_largest_first
label_desc: Use image node_id 1 for calling a global function with example usage: group_observables(observables, coefficients, grouping_type, method) and returns: partitioned_paulis,  partitioned_coeffs, partitioned_paulis