code: def testCauchyCauchyKLWithAnalytic(self):
      batch_size = 6
      mu_a = np.array([3.0] * batch_size)
      gamma_a = np.array([1.0, 2.0, 3.0, 1.5, 2.5, 3.5])
      mu_b = np.array([-3.0] * batch_size)
      gamma_b = np.array([0.5, 1.0, 1.5, 2.0, 2.5, 3.0])
  
      c_a = cauchy.Cauchy(loc=mu_a, scale=gamma_a, validate_args=True)
      c_b = cauchy.Cauchy(loc=mu_b, scale=gamma_b, validate_args=True)
  
      kl = kullback_leibler.kl_divergence(c_a, c_b)
      reverse_kl = kullback_leibler.kl_divergence(c_b, c_a)
      kl_val = self.evaluate(kl)
      reverse_kl_val = self.evaluate(reverse_kl)
  
      kl_expected = np.log(
          (gamma_a + gamma_b) ** 2 + (mu_a - mu_b) ** 2
      ) - np.log(4.0 * gamma_a * gamma_b)
  
      self.assertEqual(kl.shape, (batch_size,))
  
      # The Cauchy KL is symmetric
      self.assertAllClose(kl_val, kl_expected)
      self.assertAllClose(reverse_kl_val, kl_expected)
  
imports: import numpy
  from scipy import stats
  import tensorflow.compat.v1
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import cauchy
  from tensorflow_probability.python.distributions import kullback_leibler
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math import gradient
label_desc: Use image node_id 30 for calling the CauchyTest obj's underlying member method code with example usage: obj.testCauchyCauchyKLWithAnalytic() without return types