docs: def expectation_sensitivity(T, a):
      r"""Sensitivity of expectation value of observable A=(a_i).
  
      Parameters
      ----------
      T : (M, M) ndarray
          Transition matrix
      a : (M,) ndarray
          Observable, a[i] is the value of the observable at state i.
  
      Returns
      -------
      S : (M, M) ndarray
          Sensitivity matrix of the expectation value.
  
      """
      M = T.shape[0]
      S = numpy.zeros((M, M))
      for i in range(M):
          S += a[i] * stationary_distribution_sensitivity(T, i)
      return S