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import math |
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from numbers import Real |
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from numbers import Number |
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import torch |
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from torch.distributions import constraints |
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from torch.distributions.exp_family import ExponentialFamily |
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from torch.distributions.utils import _standard_normal, broadcast_all |
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__all__ = ['Normal'] |
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class Normal(ExponentialFamily): |
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r""" |
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Creates a normal (also called Gaussian) distribution parameterized by |
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:attr:`loc` and :attr:`scale`. |
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Example:: |
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>>> # xdoctest: +IGNORE_WANT("non-deterinistic") |
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>>> m = Normal(torch.tensor([0.0]), torch.tensor([1.0])) |
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>>> m.sample() # normally distributed with loc=0 and scale=1 |
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tensor([ 0.1046]) |
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Args: |
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loc (float or Tensor): mean of the distribution (often referred to as mu) |
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scale (float or Tensor): standard deviation of the distribution |
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(often referred to as sigma) |
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""" |
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arg_constraints = {'loc': constraints.real, 'scale': constraints.positive} |
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support = constraints.real |
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has_rsample = True |
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_mean_carrier_measure = 0 |
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@property |
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def mean(self): |
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return self.loc |
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@property |
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def mode(self): |
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return self.loc |
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@property |
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def stddev(self): |
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return self.scale |
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@property |
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def variance(self): |
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return self.stddev.pow(2) |
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def __init__(self, loc, scale, validate_args=None): |
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self.loc, self.scale = broadcast_all(loc, scale) |
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if isinstance(loc, Number) and isinstance(scale, Number): |
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batch_shape = torch.Size() |
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else: |
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batch_shape = self.loc.size() |
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super(Normal, self).__init__(batch_shape, validate_args=validate_args) |
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def expand(self, batch_shape, _instance=None): |
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new = self._get_checked_instance(Normal, _instance) |
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batch_shape = torch.Size(batch_shape) |
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new.loc = self.loc.expand(batch_shape) |
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new.scale = self.scale.expand(batch_shape) |
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super(Normal, new).__init__(batch_shape, validate_args=False) |
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new._validate_args = self._validate_args |
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return new |
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def sample(self, sample_shape=torch.Size()): |
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shape = self._extended_shape(sample_shape) |
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with torch.no_grad(): |
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return torch.normal(self.loc.expand(shape), self.scale.expand(shape)) |
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def rsample(self, sample_shape=torch.Size()): |
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shape = self._extended_shape(sample_shape) |
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eps = _standard_normal(shape, dtype=self.loc.dtype, device=self.loc.device) |
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return self.loc + eps * self.scale |
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def log_prob(self, value): |
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if self._validate_args: |
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self._validate_sample(value) |
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var = (self.scale ** 2) |
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log_scale = math.log(self.scale) if isinstance(self.scale, Real) else self.scale.log() |
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return -((value - self.loc) ** 2) / (2 * var) - log_scale - math.log(math.sqrt(2 * math.pi)) |
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def cdf(self, value): |
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if self._validate_args: |
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self._validate_sample(value) |
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return 0.5 * (1 + torch.erf((value - self.loc) * self.scale.reciprocal() / math.sqrt(2))) |
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def icdf(self, value): |
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return self.loc + self.scale * torch.erfinv(2 * value - 1) * math.sqrt(2) |
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def entropy(self): |
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return 0.5 + 0.5 * math.log(2 * math.pi) + torch.log(self.scale) |
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@property |
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def _natural_params(self): |
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return (self.loc / self.scale.pow(2), -0.5 * self.scale.pow(2).reciprocal()) |
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def _log_normalizer(self, x, y): |
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return -0.25 * x.pow(2) / y + 0.5 * torch.log(-math.pi / y) |
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