torch.distributions.studentT 的源代码

import math

import torch
from torch import inf, nan
from torch.distributions import Chi2, constraints
from torch.distributions.distribution import Distribution
from torch.distributions.utils import _standard_normal, broadcast_all

__all__ = ["StudentT"]


class StudentT(Distribution):
    r"""
    创建一个由自由度 :attr:`df`、均值 :attr:`loc` 和尺度 :attr:`scale` 参数化的学生 t 分布。

    示例::

        >>> # xdoctest: +IGNORE_WANT("非确定性")
        >>> m = StudentT(torch.tensor([2.0]))
        >>> m.sample()  # 自由度为 2 的学生 t 分布
        tensor([ 0.1046])

    参数:
        df (float 或 Tensor): 自由度
        loc (float 或 Tensor): 分布的均值
        scale (float 或 Tensor): 分布的尺度
    """
    arg_constraints = {
        "df": constraints.positive,
        "loc": constraints.real,
        "scale": constraints.positive,
    }
    support = constraints.real
    has_rsample = True

    @property
    def mean(self):
        m = self.loc.clone(memory_format=torch.contiguous_format)
        m[self.df <= 1] = nan
        return m

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

    @property
    def variance(self):
        m = self.df.clone(memory_format=torch.contiguous_format)
        m[self.df > 2] = (
            self.scale[self.df > 2].pow(2)
            * self.df[self.df > 2]
            / (self.df[self.df > 2] - 2)
        )
        m[(self.df <= 2) & (self.df > 1)] = inf
        m[self.df <= 1] = nan
        return m

    def __init__(self, df, loc=0.0, scale=1.0, validate_args=None):
        self.df, self.loc, self.scale = broadcast_all(df, loc, scale)
        self._chi2 = Chi2(self.df)
        batch_shape = self.df.size()
        super().__init__(batch_shape, validate_args=validate_args)

    def expand(self, batch_shape, _instance=None):
        new = self._get_checked_instance(StudentT, _instance)
        batch_shape = torch.Size(batch_shape)
        new.df = self.df.expand(batch_shape)
        new.loc = self.loc.expand(batch_shape)
        new.scale = self.scale.expand(batch_shape)
        new._chi2 = self._chi2.expand(batch_shape)
        super(StudentT, new).__init__(batch_shape, validate_args=False)
        new._validate_args = self._validate_args
        return new

    def rsample(self, sample_shape=torch.Size()):
        # 注意：这与 scipy 实现不完全一致。
        # (参见 https://github.com/fritzo/notebooks/blob/master/debug-student-t.ipynb)。使用 DoubleTensor
        # 参数似乎