text: import math
  
  from torch._six import inf
  from torch.distributions import constraints
  from torch.distributions.transforms import AbsTransform
  from torch.distributions.normal import Normal
  from torch.distributions.transformed_distribution import TransformedDistribution
  
  
  class HalfNormal(TransformedDistribution):
      r"""
      Creates a half-normal distribution parameterized by `scale` where::
  
          X ~ Normal(0, scale)
          Y = |X| ~ HalfNormal(scale)
  
      Example::
  
          >>> m = HalfNormal(torch.tensor([1.0]))
          >>> m.sample()  # half-normal distributed with scale=1
          tensor([ 0.1046])
  
      Args:
          scale (float or Tensor): scale of the full Normal distribution
      """
      arg_constraints = {'scale': constraints.positive}
      support = constraints.positive
      has_rsample = True
  
      def __init__(self, scale, validate_args=None):
          base_dist = Normal(0, scale)
          super(HalfNormal, self).__init__(base_dist, AbsTransform(),
                                           validate_args=validate_args)
  
      def expand(self, batch_shape, _instance=None):
          new = self._get_checked_instance(HalfNormal, _instance)
          return super(HalfNormal, self).expand(batch_shape, _instance=new)
  
      @property
      def scale(self):
          return self.base_dist.scale
  
      @property
      def mean(self):
          return self.scale * math.sqrt(2 / math.pi)
  
      @property
      def variance(self):
          return self.scale.pow(2) * (1 - 2 / math.pi)
  
      def log_prob(self, value):
          log_prob = self.base_dist.log_prob(value) + math.log(2)
          log_prob[value.expand(log_prob.shape) < 0] = -inf
          return log_prob
  
      def cdf(self, value):
          return 2 * self.base_dist.cdf(value) - 1
  
      def icdf(self, prob):
          return self.base_dist.icdf((prob + 1) / 2)
  
      def entropy(self):
          return self.base_dist.entropy() - math.log(2)
  