How to index and find the resulting matrix?

Hello

There is a mesh where I have the coordinates of the centres of each element as seen in this image (16 elements in total where the distance between centres of neighbouring elements is always 0.5 m either in veritcal or horizontal directions )

If I want to find the correlation matrix, I have to calculate this formula between every two elements of the mesh:

rho(element1, element2) = exp(-sqrt(2*(xi-xj)/tx)^2+(2*(yi-yj)/ty)^2)

where tx=200 and ty=1.5.

I need guidance regarding the indexing, as correlation between elemets 1 and 3 differs from the correlation between elements 1 and 9 . In other words, how to write a for loop to find the rho matrix which contains correlation between different elements?

The problem is relating the label of the element to the i and j coordinates !

Answer 1

[Dyuman Joshi]

[x,y]=meshgrid(0.25:0.5:1.75);
%Transposing as linear indexing in MATLAB is column wise
x=x'

x = 4×4

0.2500 0.2500 0.2500 0.2500 0.7500 0.7500 0.7500 0.7500 1.2500 1.2500 1.2500 1.2500 1.7500 1.7500 1.7500 1.7500

y=y'

y = 4×4

0.2500 0.7500 1.2500 1.7500 0.2500 0.7500 1.2500 1.7500 0.2500 0.7500 1.2500 1.7500 0.2500 0.7500 1.2500 1.7500

%Required output is 16x16 matrix
s=size(x).^2;
%Preallocation
out=zeros(s);


tx=200;
ty=1.5;
%Defining formula as a function handle 
rho = @(xi,xj,yi,yj) exp(-sqrt(2*(xi-xj)/tx)^2+(2*(yi-yj)/ty)^2);
%Note the order of input

%Double for loop, to go through each pair of elements
for idx=1:s(1)
    for jdx=1:s(2)
        out(idx,jdx)=rho(x(idx),x(jdx),y(idx),y(jdx));
    end
end
disp(out)

    1.0000    1.0050    1.0101    1.0151    1.5596    1.5674    1.5753    1.5832    5.9167    5.9464    5.9762    6.0061   54.5982   54.8718   55.1469   55.4233
    0.9950    1.0000    1.0050    1.0101    1.5518    1.5596    1.5674    1.5753    5.8872    5.9167    5.9464    5.9762   54.3258   54.5982   54.8718   55.1469
    0.9900    0.9950    1.0000    1.0050    1.5441    1.5518    1.5596    1.5674    5.8578    5.8872    5.9167    5.9464   54.0549   54.3258   54.5982   54.8718
    0.9851    0.9900    0.9950    1.0000    1.5364    1.5441    1.5518    1.5596    5.8286    5.8578    5.8872    5.9167   53.7853   54.0549   54.3258   54.5982
    1.5596    1.5674    1.5753    1.5832    1.0000    1.0050    1.0101    1.0151    1.5596    1.5674    1.5753    1.5832    5.9167    5.9464    5.9762    6.0061
    1.5518    1.5596    1.5674    1.5753    0.9950    1.0000    1.0050    1.0101    1.5518    1.5596    1.5674    1.5753    5.8872    5.9167    5.9464    5.9762
    1.5441    1.5518    1.5596    1.5674    0.9900    0.9950    1.0000    1.0050    1.5441    1.5518    1.5596    1.5674    5.8578    5.8872    5.9167    5.9464
    1.5364    1.5441    1.5518    1.5596    0.9851    0.9900    0.9950    1.0000    1.5364    1.5441    1.5518    1.5596    5.8286    5.8578    5.8872    5.9167
    5.9167    5.9464    5.9762    6.0061    1.5596    1.5674    1.5753    1.5832    1.0000    1.0050    1.0101    1.0151    1.5596    1.5674    1.5753    1.5832
    5.8872    5.9167    5.9464    5.9762    1.5518    1.5596    1.5674    1.5753    0.9950    1.0000    1.0050    1.0101    1.5518    1.5596    1.5674    1.5753
    5.8578    5.8872    5.9167    5.9464    1.5441    1.5518    1.5596    1.5674    0.9900    0.9950    1.0000    1.0050    1.5441    1.5518    1.5596    1.5674
    5.8286    5.8578    5.8872    5.9167    1.5364    1.5441    1.5518    1.5596    0.9851    0.9900    0.9950    1.0000    1.5364    1.5441    1.5518    1.5596
   54.5982   54.8718   55.1469   55.4233    5.9167    5.9464    5.9762    6.0061    1.5596    1.5674    1.5753    1.5832    1.0000    1.0050    1.0101    1.0151
   54.3258   54.5982   54.8718   55.1469    5.8872    5.9167    5.9464    5.9762    1.5518    1.5596    1.5674    1.5753    0.9950    1.0000    1.0050    1.0101
   54.0549   54.3258   54.5982   54.8718    5.8578    5.8872    5.9167    5.9464    1.5441    1.5518    1.5596    1.5674    0.9900    0.9950    1.0000    1.0050
   53.7853   54.0549   54.3258   54.5982    5.8286    5.8578    5.8872    5.9167    1.5364    1.5441    1.5518    1.5596    0.9851    0.9900    0.9950    1.0000

Here out(X,Y) will correspond to correlation of Xth andYth elements.

[Pooneh Shah Malekpoor]

Thanks for your response. but it doesnot yield correct result:

assume the correlation between first and second element:

then:

rho(1,2)=exp(-sqrt((2*(0.25-0.75))/tx)^2+(2*(0.25-0.25))/ty)^2)=0.995 not 1.5596

[Pooneh Shah Malekpoor]

Resolved! Thanks