# how to define the factorial if data set is non-integer

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mohd akmal masud le 20 Sep 2023
Commenté : Dyuman Joshi le 16 Oct 2023
dear all
I have the data set as attached, and the formula as picture below.
I want to calculat the probabilty certain point using the formula as below.
My problem is how to define my factorial, while my data is non-integer.
clc
clear all
close all
sz = [128 128 64];
fname = 'jaszak18092023tc10n1bckg10mbq10jutaf.a00';
fid = fopen(fname);
data = fread(fid,'*float'); % assuming uint
fclose(fid);
% this is blindly devectorized
% may still be transposed, but i can't tell due to symmetry
% note that data is unit-scale single-precision float
data = reshape(data,sz);
%% TO GET THE MEAN DATA SET
lamda = mean(mean(mean(data)));
% lamda = 0.0223; % lamda REPRESENT mean data set, I got from my data set
e = 2.718; % Euler number (exp)
k = 0.439173; % LET SAY my point to calculate the P (probability) (THE VALUE K FROM MY DATA SET, THE COORDINATE IS , [65 64 1])
j=factorial(k);
P = (lamda^k * exp(-lamda)/factorial(k));
Error using factorial
N must be an array of real non-negative integers.
ANYONE CAN HELP ME?
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mohd akmal masud le 21 Sep 2023
Dear @Bruno Luong, you are very correct
Dyuman Joshi le 16 Oct 2023
Both the answers provided here do not understand nor acknowledge the problem with what OP is trying to do.
The comments above by Bruno and dpb have pointed out what the mistake is.

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### Réponse acceptée

Akshat Dalal le 8 Oct 2023
Hi Akmal,
The factorial operation is only defined for integral values. However, there are extensions to the concept of factorial for non-integer values. One such extension is the gamma function, which can be used to define the factorial for non-integer values. Mathematically,
You can use the inbuilt ‘gamma’ function in MATLAB to calculate factorials of non-integral values.
For more information on using the gamma function in MATLAB, please refer the following documentation - https://in.mathworks.com/help/releases/R2023b/symbolic/gamma.html
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### Plus de réponses (1)

Francis Mike John Camogao le 14 Oct 2023
Modifié(e) : Francis Mike John Camogao le 14 Oct 2023
The error you are encountering is because the `factorial` function expects the input `k` to be a non-negative integer, but you are providing it with a floating-point value. To calculate the factorial of a floating-point number, you need to modify the code. You can use the `gamma` function, which calculates the factorial of a real number (including floating-point values). Here's how you can modify your code to fix the error:
clc
clear all
close all
sz = [128 128 64];
fname = 'jaszak18092023tc10n1bckg10mbq10jutaf.a00';
fid = fopen(fname);
data = fread(fid,'*float'); % assuming uint
fclose(fid);
% this is blindly devectorized
% may still be transposed, but I can't tell due to symmetry
% note that data is unit-scale single-precision float
data = reshape(data, sz);
%% TO GET THE MEAN DATA SET
lamda = mean(mean(mean(data)));
% lamda = 0.0223; % lamda REPRESENT mean data set, I got from my data set
e = 2.718; % Euler number (exp)
k = 0.439173; % LET SAY my point to calculate the P (probability) (THE VALUE K FROM MY DATA SET, THE COORDINATE IS , [65 64 1])
% Calculate factorial using gamma function
j = gamma(k + 1);
P = (lamda^k * exp(-lamda) / j);
% Display the result
fprintf('P = %f\n', P);
I also got and implemented the ideas atop my response.
In this code, I replaced the `factorial` function with the `gamma` function to calculate the factorial of `k`, which is a floating-point number. This should resolve the error you were encountering. I as well modifed, added some lines.
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