PyTorch 阶乘函数

Question

PyTorch 似乎没有计算阶乘的函数。 PyTorch 有没有办法做到这一点？我希望在 Torch 中手动计算泊松分布（我知道存在这种分布：https://pytorch.org/docs/stable/ generated/torch.poisson.html）并且该公式需要分母中的阶乘。

泊松分布：https://en.wikipedia.org/wiki/Poisson_distribution

Answer 1

我认为你可以找到它

torch.jit._builtins.math.factorial

BUT

pytorch

以及

numpy

和

scipy

（numpy 和 scipy 中的阶乘）使用

python

的内置

math.factorial

:

import math

import numpy as np
import scipy as sp
import torch


print(torch.jit._builtins.math.factorial is math.factorial)
print(np.math.factorial is math.factorial)
print(sp.math.factorial is math.factorial)

True
True
True

但是，相比之下，

scipy

除了“主流”

math.factorial

之外，还包含非常“特殊”的阶乘函数

scipy.special.factorial

。与

math

模块中的函数不同，它在数组上运行：

from scipy import special

print(special.factorial is math.factorial)

False

# the all known factorial functions
factorials = (
    math.factorial,
    torch.jit._builtins.math.factorial,
    np.math.factorial,
    sp.math.factorial,
    special.factorial,
)

# Let's run some tests
tnsr = torch.tensor(3)

for fn in factorials:
    try:
        out = fn(tnsr)
    except Exception as err:
        print(fn.__name__, fn.__module__, ':', err)
    else:
        print(fn.__name__, fn.__module__, ':', out)

factorial math : 6
factorial math : 6
factorial math : 6
factorial math : 6
factorial scipy.special._basic : tensor(6., dtype=torch.float64)

tnsr = torch.tensor([1, 2, 3])

for fn in factorials:
    try:
        out = fn(tnsr)
    except Exception as err:
        print(fn.__name__, fn.__module__, ':', err)
    else:
        print(fn.__name__, fn.__module__, ':', out)

factorial math : only integer tensors of a single element can be converted to an index
factorial math : only integer tensors of a single element can be converted to an index
factorial math : only integer tensors of a single element can be converted to an index
factorial math : only integer tensors of a single element can be converted to an index
factorial scipy.special._basic : tensor([1., 2., 6.], dtype=torch.float64)

Answer 2

内置

math

模块 (docs) 提供了一个函数，该函数将给定积分的阶乘返回为

int

。

import math

x = math.factorial(5)
print(x)
print(type(x))

输出

120
<class 'int'>

Answer 3

torch.lgamma

计算伽玛的对数，等于 (x-1)！

import torch

def log_factorial(x):
  return torch.lgamma(x + 1)

def factorial(x):
  return torch.exp(log_factorial(x))