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# Source code for torch.distributions.normal

    import math
    from numbers import Number, Real

    import torch
    from torch.distributions import constraints
    from torch.distributions.exp_family import ExponentialFamily
    from torch.distributions.utils import _standard_normal, broadcast_all

    __all__ = ["Normal"]

    class Normal(ExponentialFamily):
        r"""
        Creates a normal (also called Gaussian) distribution parameterized by
        :attr:`loc` and :attr:`scale`.

        Example::

            >>> # xdoctest: +IGNORE_WANT("non-deterinistic")
            >>> m = Normal(torch.tensor([0.0]), torch.tensor([1.0]))
            >>> m.sample()  # normally distributed with loc=0 and scale=1
            tensor([ 0.1046])

        Args:
            loc (float or Tensor): mean of the distribution (often referred to as mu)
            scale (float or Tensor): standard deviation of the distribution
                (often referred to as sigma)
        """
        arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
        support = constraints.real
        has_rsample = True
        _mean_carrier_measure = 0

        @property
        def mean(self):
            return self.loc

        @property
        def mode(self):
            return self.loc

        @property
        def stddev(self):
            return self.scale

        @property
        def variance(self):
            return self.stddev.pow(2)

        def __init__(self, loc, scale, validate_args=None):
            self.loc, self.scale = broadcast_all(loc, scale)
            if isinstance(loc, Number) and isinstance(scale, Number):
                batch_shape = torch.Size()
            else:
                batch_shape = self.loc.size()
            super().__init__(batch_shape, validate_args=validate_args)

        def expand(self, batch_shape, _instance=None):
            new = self._get_checked_instance(Normal, _instance)
            batch_shape = torch.Size(batch_shape)
            new.loc = self.loc.expand(batch_shape)
            new.scale = self.scale.expand(batch_shape)
            super(Normal, new).__init__(batch_shape, validate_args=False)
            new._validate_args = self._validate_args
            return new

        def sample(self, sample_shape=torch.Size()):
            shape = self._extended_shape(sample_shape)
            with torch.no_grad():
                return torch.normal(self.loc.expand(shape), self.scale.expand(shape))

        def rsample(self, sample_shape=torch.Size()):
            shape = self._extended_shape(sample_shape)
            eps = _standard_normal(shape, dtype=self.loc.dtype, device=self.loc.device)
            return self.loc + eps * self.scale

        def log_prob(self, value):
            if self._validate_args:
                self._validate_sample(value)
            # compute the variance
            var = self.scale**2
            log_scale = (
                math.log(self.scale) if isinstance(self.scale, Real) else self.scale.log()
            )
            return (
                -((value - self.loc) ** 2) / (2 * var)
                - log_scale
                - math.log(math.sqrt(2 * math.pi))
            )

        def cdf(self, value):
            if self._validate_args:
                self._validate_sample(value)
            return 0.5 * (
                1 + torch.erf((value - self.loc) * self.scale.reciprocal() / math.sqrt(2))
            )

        def icdf(self, value):
            return self.loc + self.scale * torch.erfinv(2 * value - 1) * math.sqrt(2)

        def entropy(self):
            return 0.5 + 0.5 * math.log(2 * math.pi) + torch.log(self.scale)

        @property
        def _natural_params(self):
            return (self.loc / self.scale.pow(2), -0.5 * self.scale.pow(2).reciprocal())

        def _log_normalizer(self, x, y):
            return -0.25 * x.pow(2) / y + 0.5 * torch.log(-math.pi / y)

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