PyTorch Factorial Function

Question

There does not seem to be a PyTorch function for computing a factorial. Is there a method to do this in PyTorch? I am looking to manually compute a Poisson distribution in Torch (I am aware this exists: https://pytorch.org/docs/stable/generated/torch.poisson.html) and the formula requires a factorial in the denominator.

Poisson Distribution: https://en.wikipedia.org/wiki/Poisson_distribution

Answer 1

I think you can find it as torch.jit._builtins.math.factorial BUT pytorch as well as numpy and scipy (Factorial in numpy and scipy) uses python's builtin 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

But, in contrast, scipy in addition to "mainstream" math.factorial contains the very "special" factorial function scipy.special.factorial. Unlike function from math module it operates on arrays:

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)