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

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

Answer 1

[Davide Masiello]

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.

[Andy]

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]

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

Answer 2

[David Hill]

Use the gamma function.

gamma(1.3);

Answer 3

[DGM]

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