How to make a summation with index vector?

Hi! I need to solve this summation in Matlab:

where N is a constant and s is a matrix YxN. I tried to use symsum function but I can't index the s matrix. Anyone can help me? Many thanks!

[Aditya Salveru]

can you please provide an example?

[Walter Roberson]

If s is Y x N then what is s subscript t ?

[Adriano]

Sorry the matrix is a TxN. I'm working with a time serie so that the row is usually indicated with t. Suppose I have a matrix like:

s = [1 2; 3 4; 5 6] where N = size(s,2)

I need to create a vector Z in which the first element is:

value_1_1 = (1*s(1,1) - (1/N)) + (2*s(1,2) - (2/N));

the second one is:

value_2_1 = (1*s(2,1) - (1/N)) + (2*s(2,2) - (2/N));

and so on. Obviously in the reality the s matrix is a very large matrix so that I need a simple way to calculate it.

Answer 1

[Guillaume]

I need to create a vector Z in which the first element is:

col = 1:size(s, 2);
Z = sum(col .* s - col/N, 2);  %requires R2016b or later

Note that the sum 1/N + ... N/N could be extracted from the formula since it's a constant equal to (N+1)/2, so a simplification of the above would be:

Z = sum(col .* s) - (size(s, 2)+1)/2;