code: def interpolate_backward_differences(
      backward_differences, order, step_size_ratio
  ):
      """Updates backward differences when a change in the step size occurs."""
      state_dtype = backward_differences.dtype
      interpolation_matrix_ = interpolation_matrix(
          state_dtype, order, step_size_ratio
      )
      interpolation_matrix_unit_step_size_ratio = interpolation_matrix(
          state_dtype, order, 1.0
      )
      interpolated_backward_differences_orders_one_to_five = tf.matmul(
          interpolation_matrix_unit_step_size_ratio,
          tf.matmul(
              interpolation_matrix_,
              backward_differences[1 : MAX_ORDER + 1],
          ),
      )
      interpolated_backward_differences = tf.concat(
          [
              tf.gather(backward_differences, [0]),
              interpolated_backward_differences_orders_one_to_five,
              ps.zeros(
                  ps.stack([2, ps.shape(backward_differences)[1]]),
                  dtype=state_dtype,
              ),
          ],
          0,
      )
      return interpolated_backward_differences
  
file_path: probability/tensorflow_probability/python/math/ode/bdf_util.py
imports: import collections
  import numpy
  import tensorflow.compat.v1
  import tensorflow.compat.v2
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import tensorshape_util
label_desc: Use image node_id 3 for calling a global function with example usage: interpolate_backward_differences(backward_differences, order, step_size_ratio) and returns: interpolated_backward_differences