code: def testFiniteGradientAtDifficultPoints(self):
      for dtype in [np.float32, np.float64]:
          loc = tf.Variable(dtype(0.0))
          scale = tf.Variable(dtype(1.0))
          x = np.array(
              [-100.0, -20.0, -5.0, 0.0, 5.0, 20.0, 100.0]
          ).astype(dtype)
  
          def cauchy_function(name, x):
              def _cauchy(loc, scale):
                  return getattr(
                      cauchy.Cauchy(
                          loc=loc, scale=scale, validate_args=True
                      ),
                      name,
                  )(x)
  
              return _cauchy
  
          self.evaluate([loc.initializer, scale.initializer])
          for func_name in [
              "cdf",
              "log_cdf",
              "survival_function",
              "log_survival_function",
              "log_prob",
              "prob",
          ]:
              value, grads = self.evaluate(
                  gradient.value_and_gradient(
                      cauchy_function(func_name, x), [loc, scale]
                  )
              )
              self.assertAllFinite(value)
              self.assertAllFinite(grads[0])
              self.assertAllFinite(grads[1])
  
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 12 for calling the CauchyTest obj's underlying member method code with example usage: obj.testFiniteGradientAtDifficultPoints() and returns: _cauchy, getattr