code: def test_gluon_cauchy():
      class TestCauchy(HybridBlock):
          def __init__(self, func):
              self._func = func
              super(TestCauchy, self).__init__()
  
          def forward(self, loc, scale, *args):
              cauchy = mgp.Cauchy(loc, scale, validate_args=True)
              return _distribution_method_invoker(
                  cauchy, self._func, *args
              )
  
      shapes = [(), (1,), (2, 3), 6]
  
      # Test sampling
      for shape, hybridize in itertools.product(shapes, [True, False]):
          loc = np.random.uniform(-1, 1, shape)
          scale = np.random.uniform(0.5, 1.5, shape)
          samples = np.random.normal(size=shape)
          net = TestCauchy("sample")
          if hybridize:
              net.hybridize()
          mx_out = net(loc, scale)
          desired_shape = (
              (shape,) if isinstance(shape, Number) else shape
          )
          assert mx_out.shape == desired_shape
  
      # Test log_prob
      for shape, hybridize in itertools.product(shapes, [True, False]):
          loc = np.random.uniform(-1, 1, shape)
          scale = np.random.uniform(0.5, 1.5, shape)
          samples = np.random.normal(size=shape)
          net = TestCauchy("log_prob")
          if hybridize:
              net.hybridize()
          mx_out = net(loc, scale, samples).asnumpy()
          np_out = ss.cauchy(loc.asnumpy(), scale.asnumpy()).logpdf(
              samples.asnumpy()
          )
          assert_almost_equal(
              mx_out, np_out, atol=1e-4, rtol=1e-3, use_broadcast=False
          )
  
      # Test cdf
      for shape, hybridize in itertools.product(shapes, [True, False]):
          loc = np.random.uniform(-1, 1, shape)
          scale = np.random.uniform(0.5, 1.5, shape)
          samples = np.random.normal(size=shape)
          net = TestCauchy("cdf")
          if hybridize:
              net.hybridize()
          mx_out = net(loc, scale, samples).asnumpy()
          np_out = ss.cauchy(loc.asnumpy(), scale.asnumpy()).cdf(
              samples.asnumpy()
          )
          assert_almost_equal(
              mx_out, np_out, atol=1e-4, rtol=1e-3, use_broadcast=False
          )
  
      # Test icdf
      for shape, hybridize in itertools.product(shapes, [True, False]):
          loc = np.random.uniform(-1, 1, shape)
          scale = np.random.uniform(0.5, 1.5, shape)
          samples = np.random.uniform(
              size=shape, low=1e-4, high=1.0 - 1e-4
          )
          net = TestCauchy("icdf")
          if hybridize:
              net.hybridize()
          mx_out = net(loc, scale, samples).asnumpy()
          np_out = ss.cauchy(loc.asnumpy(), scale.asnumpy()).ppf(
              samples.asnumpy()
          )
          assert_almost_equal(
              mx_out, np_out, atol=1e-4, rtol=1e-3, use_broadcast=False
          )
  
      # Test entropy
      for shape, hybridize in itertools.product(shapes, [True, False]):
          loc = np.random.uniform(-1, 1, shape)
          scale = np.random.uniform(0.5, 1.5, shape)
          net = TestCauchy("entropy")
          if hybridize:
              net.hybridize()
          mx_out = net(loc, scale).asnumpy()
          np_out = ss.cauchy(loc.asnumpy(), scale.asnumpy()).entropy()
          assert_almost_equal(
              mx_out, np_out, atol=1e-4, rtol=1e-3, use_broadcast=False
          )
  
imports: import mxnet
  import numpy
  from mxnet import np, npx, autograd
  from mxnet import gluon
  import mxnet.gluon.probability
  from mxnet.gluon.probability import StochasticBlock, StochasticSequential
  from mxnet.gluon import HybridBlock
  from mxnet.test_utils import use_np, assert_almost_equal
  from numpy.testing import assert_array_equal
  import pytest
  import scipy.stats
  import scipy.special
  import itertools
  from numbers import Number
label_desc: Use image node_id 6 for calling a global function with example usage: test_gluon_cauchy() and returns: _distribution_method_invoker