Problem with matrices operations

My Matlab knowledge is minimal and I was hoping someone could help me. I have generated two 4x900 size matrices. The matrices are X and Y. The operation that I must carry out is the following:

N=900

R(1)=(X(1st column)-Y(1st column))*transpose(X(1st column)-Y(1st column))
R(2)=(X(2nd column)-Y(2nd column))*transpose(X(2nd column)-Y(2nd column))
% ...
R(N)=(X(Nth column)-Y(Nth column))*transpose(X(Nth column)-Y(Nth column))

R_total=sum(R(1)+R(2)+...+R(N))

As an example, it would be something like this:

N=5;

X = [1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5];
Y = [5 6 7 8 9; 5 6 7 8 9; 5 6 7 8 9; 5 6 7 8 9];

R(1)=([1;1;1;1]-[5;5;5;5])*transpose([1;1;1;1]-[5;5;5;5]);

R(2)=([2;2;2;2]-[6;6;6;6])*transpose([2;2;2;2]-[6;6;6;6]);

% ...
    
R(5)=([5;5;5;5]-[9;9;9;9])*transpose([5;5;5;5]-[9;9;9;9])

R_total=sum(R(1)+R(2)+...+R(N));

The matrices R(1), R(2), ..., R(N) y R_total must have a size of 4x4.

I have been trying to use a 'while', but I don't know how to perform the operation. Does anyone know how I could solve it? I know I have comitted some errors calling R(1), R(2)...R(N).

Sorry if the process is not clear. I have tried to explain the operations as well as I could. If someone needs any extra information, please, tell me.

Thank you!

Answer 1

[Sriram Tadavarty]

Hi,

You can try the following:

x = rand(4,900);
y = rand(4,900);

sumOut = zeros(4,4); % Updated variable name to make it different from inbuilt function
for i = 1:900
    tmp = x(:,i)-y(:,i);
    R(:,:,i) = tmp*tmp';
    sumOut = sumOut + R(:,:,i);
end

Hope this helps.

Regards,

Sriram

[Stephen23]

Naming a variable sum is not recommended because this shadows the inbuilt sum function.

[Sriram Tadavarty]

Yes. you are right. Updated the variable with other name,