torch.distributions.dirichlet 的源代码

import torch
from torch.autograd import Function
from torch.autograd.function import once_differentiable
from torch.distributions import constraints
from torch.distributions.exp_family import ExponentialFamily

__all__ = ["Dirichlet"]


# 此辅助函数用于测试。
def _Dirichlet_backward(x, concentration, grad_output):
    total = concentration.sum(-1, True).expand_as(concentration)
    grad = torch._dirichlet_grad(x, concentration, total)
    return grad * (grad_output - (x * grad_output).sum(-1, True))


class _Dirichlet(Function):
    @staticmethod
    def forward(ctx, concentration):
        x = torch._sample_dirichlet(concentration)
        ctx.save_for_backward(x, concentration)
        return x

    @staticmethod
    @once_differentiable
    def backward(ctx, grad_output):
        x, concentration = ctx.saved_tensors
        return _Dirichlet_backward(x, concentration, grad_output)


class Dirichlet(ExponentialFamily):
    r"""
    创建一个由浓度参数 :attr:`concentration` 参数化的 Dirichlet 分布。

    示例::

        >>> # xdoctest: +IGNORE_WANT("非确定性")
        >>> m = Dirichlet(torch.tensor([0.5, 0.5]))
        >>> m.sample()  # 浓度为 [0.5, 0.5] 的 Dirichlet 分布
        tensor([ 0.1046,  0.8954])

    参数:
        concentration (Tensor): 分布的浓度参数
            （通常称为 alpha）
    """
    arg_constraints = {
        "concentration": constraints.independent(constraints.positive, 1)
    }
    support = constraints.simplex
    has_rsample = True

    def __init__(self, concentration, validate_args=None):
        if concentration.dim() < 1:
            raise ValueError(
                "`concentration` 参数必须至少为一维。"
            )
        self.concentration = concentration
        batch_shape, event_shape = concentration.shape[:-1], concentration.shape[-1:]
        super().__init__(batch_shape, event_shape, validate_args=validate_args)

    def expand(self, batch_shape, _instance=None):
        new = self._get_checked_instance(Dirichlet, _instance)
        batch_shape = torch.Size(batch_shape)
        new.concentration = self.concentration.expand(batch_shape + self.event_shape)
        super(Dirichlet, new).__init__(
            batch_shape, self.event_shape, validate_args=False
        )
        new._validate_args = self._validate_args
        return new

    def rsample(self, sample_shape=()):
        shape = self._extended_shape(sample_shape)
        concentration = self.concentration.expand(shape)
        return _Dirichlet.apply(concentration)

    def log_prob(self, value):
        if self._validate_args:
            self._validate_sample(value)
        return (
            torch.xlogy(self.concentration - 1.0, value).sum(-1)
            + torch.lgamma(self.concentration.sum(-1))
            - torch.lgamma(</