Why can't Matlab do the factorial of a non-integer number?

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HWIK 2022-2-6

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评论： Dyuman Joshi 2024-1-23

Hi,

I tried using the factorial function on a number with decimals and got the following error: N must be an array of real non-negative integers.

Is there an alternative so that it can calculate the factorial of a number with decimals like Excel does?

Thanks for your time

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Answer 1

Davide Masiello 2022-2-6

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编辑：Davide Masiello 2022-2-6

在 MATLAB Online 中打开

MatLab 'factorial' is coded so to work with integers only.

The generalization of a factorial is the Γ function, which is

and the relation with the factorial is

MatLab implements the Γ function. Therefore, to compute the factorial of 1.5 you can write

gamma(2.5)

Which yields 1.3293, the correct answer.

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Andy 2024-1-23

编辑：Andy 2024-1-23

Would you know how to calculate the inverse gamma function in Matlab?

f(1.3293) = 2.5.

I tried gaminv(1.3293) but it doesn't seem related. Same with gammaincinv.

I'm trying to find a real number whose factorial is equal to a number that I input.

Dyuman Joshi 2024-1-23

在 MATLAB Online 中打开

There is no function in MATLAB, in-built or a part of the toolbox, that offers that functionality directly.

(Possibly because) There is no known explicit relation or definition which can be utilized to obtain that.

However, you can try this -

%value of which the inverse is to be calculated
y = gamma(2.5)
y = 1.3293
f = @(x, val) gamma(x) - val;
out = fzero(@(x) f(x, y), 2)
out = 2.5000

But note that the inverse gamma function is not one-on-one (reference - Graph of the function provided in its wikipedia article - https://en.wikipedia.org/wiki/Inverse_gamma_function), so multiple solutions exist for each input.

The value obtained as the output depends on the initial guess -

%Finding the inverse for the same, but with initial guess as 1
fzero(@(x) f(x, y), 1)
ans = 0.6809

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Answer 2

David Hill 2022-2-6

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在 MATLAB Online 中打开

Use the gamma function.

gamma(1.3);

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Answer 3

DGM 2022-2-6

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在 MATLAB Online 中打开

See the Gamma function

https://en.wikipedia.org/wiki/Gamma_function

Or in MATLAB, gamma().

Note that if you're trying to replicate the behavior of factorial, the input is offset by 1:

factorial([2 3 4])
ans = 1×3
     2     6    24
gamma([2 2.5 3 3.2 3.6 4])
ans = 1×6
    1.0000    1.3293    2.0000    2.4240    3.7170    6.0000
gamma([2 2.5 3 3.2 3.6 4]+1) % offset by 1
ans = 1×6
    2.0000    3.3234    6.0000    7.7567   13.3813   24.0000