Calculate the sum of all the relations between a matrix components

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Hi, does anyone know how I can calculate the sum of all the relations between a matrix components? For example by having a 3*3 matrix like:
I want to calculate a relation between all the components such that:
r11=((a11-a12)/(a11+a12) + (a11-a13)/(a11+a13) + (a11-a21)/(a11+a12) + (a11-a22)/(a11+a22) + (a11-a23)/(a11+a23)+...
(a11-a31)/(a11+a31) + (a11-a32)/(a11+a32) + (a11-a33)/(a11+a33))/n;
n=8; %Number of matrix components-1 in this case
I want to do this for every components of the matrix (each component has interaction with every other components) so that I have:
I used for loop but it takes a long time and long code to calculate the results (my real matrix is 101*101). Is there any simple way to do that? Thank you.
  1 Comment
John D'Errico
John D'Errico on 26 Jun 2021
I don't see why a well written loop would take that long of a time here. Perhaps your problem is poorly written code? For example, are you naming individual variables r11, r12, etc?

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Accepted Answer

DGM on 27 Jun 2021
This could be done various ways. You could do this with loops if it's easier to understand. I'll just do this:
% example inputs
A = [1 2 3; 4 5 6; 7 8 9];
n = numel(A)-1;
F = @(x) sum((x-A)./(x+A),'all')/n; % define a function to calculate each sum
R = arrayfun(F,A) % calculate all of them
R = 3×3
-0.6428 -0.3651 -0.1726 -0.0282 0.0853 0.1773 0.2538 0.3184 0.3738
Using numbered variable names is a great way to cause problems for yourself. If you can embed indexing information within the variable name, then you can just use an array and index into it like normal.

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