code: def rk_fourth_order_interpolation_coefficients(
      y0, y1, k, dt, tableau
  ):
      """Fit an interpolating polynomial to the results of a Runge-Kutta step.
  
      Performs 4th order interpolation based on state and state derivative values
      determined in the Runge-Kutta state.
  
      Args:
        y0: State value at the start of the interval.
        y1: State value at the end of the interval.
        k: List of state values at RK k-points.
        dt: Width of the interval.
        tableau: `ButcherTableau` describing a Runge-Kutta scheme.
  
      Returns:
        coefficients: List of coefficients that interpolate the solution.
      """
      with tf.name_scope("interp_fit_rk"):
          y_mid = weighted_sum(
              [1.0, dt], [y0, weighted_sum(tableau.c_mid, k)]
          )
          f0 = k[0]
          f1 = k[-1]
          return _fourth_order_interpolation_coefficients(
              y0, y1, y_mid, f0, f1, dt
          )
  
file_path: probability/tensorflow_probability/python/math/ode/runge_kutta_util.py
imports: import collections
  import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import prefer_static
label_desc: Use image node_id 8 for calling a global function with example usage: rk_fourth_order_interpolation_coefficients(y0, y1, k, dt, tableau) and returns: _fourth_order_interpolation_coefficients