torch.distributions.kumaraswamy 的源代码

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import torch
from torch import nan
from torch.distributions import constraints
from torch.distributions.transformed_distribution import TransformedDistribution
from torch.distributions.transforms import AffineTransform, PowerTransform
from torch.distributions.uniform import Uniform
from torch.distributions.utils import broadcast_all, euler_constant

__all__ = ["Kumaraswamy"]


def _moments(a, b, n):
    """
    使用torch.lgamma计算Kumaraswamy的第n个矩
    """
    arg1 = 1 + n / a
    log_value = torch.lgamma(arg1) + torch.lgamma(b) - torch.lgamma(arg1 + b)
    return b * torch.exp(log_value)


class Kumaraswamy(TransformedDistribution):
    r"""
    从Kumaraswamy分布中采样。

    示例::

        >>> # xdoctest: +IGNORE_WANT("非确定性")
        >>> m = Kumaraswamy(torch.tensor([1.0]), torch.tensor([1.0]))
        >>> m.sample()  # 从浓度alpha=1和beta=1的Kumaraswamy分布中采样
        tensor([ 0.1729])

    参数:
        concentration1 (float或Tensor): 分布的第一个浓度参数
            (通常称为alpha)
        concentration0 (float或Tensor): 分布的第二个浓度参数
            (通常称为beta)
    """
    arg_constraints = {
        "concentration1": constraints.positive,
        "concentration0": constraints.positive,
    }
    support = constraints.unit_interval
    has_rsample = True

    def __init__(self, concentration1, concentration0, validate_args=None):
        self.concentration1, self.concentration0 = broadcast_all(
            concentration1, concentration0
        )
        finfo = torch.finfo(self.concentration0.dtype)
        base_dist = Uniform(
            torch.full_like(self.concentration0, 0),
            torch.full_like(self.concentration0, 1),
            validate_args=validate_args,
        )
        transforms = [
            PowerTransform(exponent=self.concentration0.reciprocal()),
            AffineTransform(loc=1.0, scale=-1.0),
            PowerTransform(exponent=self.concentration1.reciprocal()),
        ]
        super().__init__(base_dist, transforms, validate_args=validate_args)

    def expand(self, batch_shape, _instance=None):
        new = self._get_checked_instance(Kumaraswamy, _instance)
        new.concentration1 = self.concentration1.expand(batch_shape)
        new.concentration0 = self.concentration0.expand(batch_shape)
        return super().expand(batch_shape, _instance=new)

    @property
    def mean(self):
        return _moments(self.concentration1, self.concentration0, 1)

    @property
    def mode(self):
        # 在log空间中计算以提高数值稳定性。
        log_mode = (
            self.concentration0.reciprocal() * (-self.concentration0).log1p()
            - (-self.concentration0 * self.concentration1).log1p()
        )
        log_mode[(self.concentration0 < 1) | (self.concentration1 < 1)] = nan
        return log_mode.exp()

    @property
    def variance(self):
        return _moments(self.concentration1, self.concentration0, <span class="