code: def _kl_cauchy_cauchy(a, b, name=None):
      """Calculate the batched KL divergence KL(a || b) with a and b Cauchy.
  
      Note that this KL divergence is symmetric in its arguments.
  
      Args:
        a: instance of a Cauchy distribution object.
        b: instance of a Cauchy distribution object.
        name: Name to use for created operations.
          Default value: `None` (i.e., `'kl_cauchy_cauchy'`).
  
      Returns:
        kl_div: Batchwise KL(a || b)
  
      #### References
  
      [1] Frederic Chyzak and Frank Nielsen. A closed-form formula for the
      Kullback-Leibler divergence between Cauchy distributions.
      https://arxiv.org/abs/1905.10965
      """
      with tf.name_scope(name or "kl_cauchy_cauchy"):
          a_scale = tf.convert_to_tensor(a.scale)
          b_scale = tf.convert_to_tensor(b.scale)
          b_loc = tf.convert_to_tensor(b.loc)
          scale_sum_square = tf.math.square(a_scale + b_scale)
          loc_diff_square = tf.math.squared_difference(a.loc, b_loc)
  
          return (
              tf.math.log(scale_sum_square + loc_diff_square)
              - np.log(4.0)
              - tf.math.log(a_scale)
              - tf.math.log(b_scale)
          )
  
imports: import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import identity
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import distribution
  from tensorflow_probability.python.distributions import kullback_leibler
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import reparameterization
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import tensor_util
label_desc: Use image node_id 1 for calling a global function with example usage: _kl_cauchy_cauchy(a, b, name) and returns: unknown