How to complete summation with column vectors?

I have the following summation I need to complete. x is a column vector of Nx1 and and u is an Nx1 column vector as well. i_th component is given as below and j_th component is same. My question is firstly, do I sum only jth components since summation bounds are j=1 to N? How is this done in Matlab?

I have the code below but I have been doubting it for the last week as the rest of my code has not converged well.

N=10;

x = ones(N,1)

u=1:N
u=u'
u=(u-.5)/N  %given parameter of u

in = @(x) sum((u.*x)./(u + u))

Answer 1

[Andrei Bobrov]

Let your vectors this:

x = ones(10,1);
u = ((1:10)'-.5)/10;

Solution:

[ui,uj] = ndgrid(u);
out = ui./(ui+uj)*x(:);

Answer 2

[Gopalkrishna Bhat]

try the below code for N=4. Assuming that k is the 2nd column and there are only 4 rows.

sum=0; ui=1; k=1;

for j=1:4 sum=sum+(ui*u(j,k))/(ui+u(j,k)); end

[Stephen23]

Never call a variable sum, as this is the name of an inbuilt function sum. This is a really bad idea, do not do this.