code: def make_periodic_input_warping(
      period, periodic_index, include_original
  ):
      """Return an input warping function that adds Fourier features.
  
      Args:
        period: The added features will repeat this many time steps.
        periodic_index: Look for the time feature in input[..., periodic_index].
        include_original: If true, don't replace the time feature with the
          new Fourier features.
  
      Returns:
        A function that takes an input tensor of shape [..., n] and returns a
        tensor of shape [..., n+2] if include_original is True and of shape
        [..., n+1] if include_original is False.
      """
  
      def input_warping(x):
          time = x[..., periodic_index]
          y = 2.0 * jnp.pi * time / period
          features = [jnp.cos(y), jnp.sin(y)]
          if include_original:
              features.append(time)
          if jnp.ndim(x) == 1:
              features = jnp.array(features).T
          else:
              features = jnp.vstack(features).T
          return jnp.concatenate(
              [
                  x[..., :periodic_index],
                  features,
                  x[..., periodic_index + 1 :],
              ],
              -1,
          )
  
      return input_warping
  
imports: from flax import linen
  from flax.linen import initializers
  import jax
  import jax.numpy
  from tensorflow_probability.python.experimental.autobnn import bnn
  from tensorflow_probability.substrates.jax.distributions import lognormal
  from tensorflow_probability.substrates.jax.distributions import normal
  from tensorflow_probability.substrates.jax.distributions import student_t
  from tensorflow_probability.substrates.jax.distributions import uniform
label_desc: Use image node_id 1 for calling a global function with example usage: make_periodic_input_warping(period, periodic_index, include_original) and returns: input_warping, jnp