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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)
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