code: def optimize_measurements(
      observables,
      coefficients=None,
      grouping="qwc",
      colouring_method="rlf",
  ):
      """Partitions then diagonalizes a list of Pauli words, facilitating simultaneous measurement of
      all observables within a partition.
  
      The input list of observables are partitioned into mutually qubit-wise commuting (QWC) or
      mutually commuting partitions by approximately solving minimum clique cover on a graph where
      each observable represents a vertex. The unitaries which diagonalize the
      partitions are then found. See `arXiv:1907.03358
      <https://arxiv.org/abs/1907.03358>`_ and `arXiv:1907.09386
      <https://arxiv.org/abs/1907.09386>`_ for technical details of the QWC and
      fully-commuting measurement-partitioning approaches respectively.
  
      Args:
          observables (list[Observable]): a list of Pauli words (Pauli operation instances and Tensor
              instances thereof)
          coefficients (list[float]): a list of float coefficients, for instance the weights of
              the Pauli words comprising a Hamiltonian
          grouping (str): the binary symmetric relation to use for operator partitioning
          colouring_method (str): the graph-colouring heuristic to use in obtaining the operator
              partitions
  
      Returns:
          tuple:
  
              * list[callable]: a list of the post-rotation templates, one
                for each partition
              * list[list[Observable]]: A list of the obtained groupings. Each
                grouping is itself a list of Pauli words diagonal in the
                measurement basis.
              * list[list[float]]: A list of coefficient groupings. Each
                coefficient grouping is itself a list of the partitions
                corresponding coefficients.  Only output if coefficients are
                specified.
  
      **Example**
  
      >>> obs = [qml.PauliY(0), qml.PauliX(0) @ qml.PauliX(1), qml.PauliZ(1)]
      >>> coeffs = [1.43, 4.21, 0.97]
      >>> rotations, groupings, grouped_coeffs = optimize_measurements(obs, coeffs, 'qwc', 'rlf')
      >>> print(rotations)
      [[RY(-1.5707963267948966, wires=[0]), RY(-1.5707963267948966, wires=[1])],
       [RX(1.5707963267948966, wires=[0])]]
      >>> print(groupings)
      [[PauliZ(wires=[0]) @ PauliZ(wires=[1])], [PauliZ(wires=[0]), PauliZ(wires=[1])]]
      >>> print(grouped_coeffs)
      [[4.21], [1.43, 0.97]]
      """
  
      if coefficients is None:
          grouped_obs = group_observables(
              observables,
              grouping_type=grouping,
              method=colouring_method,
          )
      else:
          grouped_obs, grouped_coeffs = group_observables(
              observables,
              coefficients,
              grouping_type=grouping,
              method=colouring_method,
          )
  
      if grouping.lower() == "qwc":
          (
              post_rotations,
              diagonalized_groupings,
          ) = diagonalize_qwc_groupings(grouped_obs)
      else:
          raise NotImplementedError(
              f"Measurement reduction by '{grouping.lower()}' grouping not implemented."
          )
  
      if coefficients is None:
          return post_rotations, diagonalized_groupings
  
      return post_rotations, diagonalized_groupings, grouped_coeffs
  
label_desc: Use image node_id 1 for calling a global function with example usage: optimize_measurements(observables, coefficients, grouping, colouring_method) and returns: post_rotations,  diagonalized_groupings,  grouped_coeffs, post_rotations,  diagonalized_groupings