mxn and nxn matrix element-wise multiplication without for loop

I have 2 2D matrices. First one, A, is mxn where m=n*k and second one, B, is nxn. How do I do element-wise multiplication of every nxn square sub matrix of A with B without for loop? and sum all elements of every multiplied nxn matrix and get a nx1 vector? Below is what I did with for loop. I need to perform the for loop in one row.

n = 10;
k = 5;
A = rand(k*n,n);
B = rand(n,n);
results = zeros(k,1);
for i=1:k
    results(i) = sum(B.*A(1+n*(i-1):i*n,:),'all');
end

[Cris LaPierre]

I don't think your code is doing what you think it is doing. It is taking a single element from A, multiplying all elements of B by it, and then summing all the resulting values.

[ebon T]

You are right! I just edited my question. It was just an example I created for the question.

[Walter Roberson]

Does using arrayfun() count as "using a for loop" ? These days arrayfun() is implemented internally, but in the older days it was a function like any other function and included MATLAB-level for loops.

[ebon T]

Actually as long as it creates the nx1 vector in one line it is fine.

[Cris LaPierre]

What about the requirement to use elementwise multiplication and not use for loops? What about achieving this all in a single row?

[ebon T]

If the solution can provide all of these then it is perfect! If it is not possible to vectorize then one line of solution also acceptable.

Answer 1

[Bruno Luong]

AA = permute(reshape(A,[n,k,n]),[2 1 3]);
results = AA(:,:)*B(:)

[ebon T]

Thanks a lot Bruno!