Calculate the sum of all the relations between a matrix components

Question

MarshallSc 2021-6-26

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/866105-calculate-the-sum-of-all-the-relations-between-a-matrix-components

评论： MarshallSc 2021-7-8

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:

a=[a11,a12,a13;a21,a22,a23;a31,a32,a33];

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:

r12,r13,r21,r22,r23,r31,r32,r33

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 个评论
显示 -1更早的评论隐藏 -1更早的评论

John D'Errico 2021-6-26

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?

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

DGM 2021-6-27

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/866105-calculate-the-sum-of-all-the-relations-between-a-matrix-components#answer_734355

在 MATLAB Online 中打开

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.

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

3 个评论
显示 1更早的评论隐藏 1更早的评论

DGM 2021-7-8

在 MATLAB Online 中打开

I'm just going to use a loop.

A = [1 2 3; 4 5 6; 7 8 9];
B = [1 2 3; 4 5 6; 7 8 9]*10;
C = [1 2 3; 4 5 6; 7 8 9]*100;
% if you use a cell array, the relative matrix sizes don't matter
D = {A,B,C};
R = cell(size(D));
for d = 1:numel(D)
    thismat = D{d};
    n = numel(thismat)-1;
    F = @(x) sum((x-thismat)./(x+thismat),'all')/n;
    R{d} = arrayfun(F,thismat);
end
celldisp(R)
 
R{1} =
 
   -0.6428   -0.3651   -0.1726
   -0.0282    0.0853    0.1773
    0.2538    0.3184    0.3738

 
 
R{2} =
 
   -0.6428   -0.3651   -0.1726
   -0.0282    0.0853    0.1773
    0.2538    0.3184    0.3738

 
 
R{3} =
 
   -0.6428   -0.3651   -0.1726
   -0.0282    0.0853    0.1773
    0.2538    0.3184    0.3738

 