Creation of matrix using lower triangular matrix?

Hi everybody. I have a power system that gives me the vector B (containing active P and reactive power Q), and I want to get the vector S (S = A * B) as described in the figure below. Note that the vector B should not be modified. I have already used a lower triangular matrix (in A) but I trouble linking the two powers (P, Q) to obtain the apparent power as is described in the vector S.

Answer 1

[Guillaume]

I don't understand what is going in with A but the S as described is:

S = cumsum(hypot(B(1:2:end), B(2:2:end)))

[ET-TAOUSSI mehdi]

Thank you Guillaume. But I want to build the vector S from (A * B), with this I get the following result:

However I try to have the previous one result.

[ET-TAOUSSI mehdi]

The vector B contains other elements that are marked by black points. please the Vector B should not be modified and vector A can contain only null and unit matrices.

[Guillaume]

Well, A*B (let's call it T) is the sum of the Pi and Qi. Tn = ∑1...n Pi+Qi, whereas you want Sn = ∑1...n sqrt(Pi^2+Qi^2). You can't express S solely in term of T so what you're asking is not possible.

Now that I understand what A is about, this is how I would do it:

PQ = B(logical(A(end, :)); %Extract P and Q from B
S = cumsum(hypot(PQ(1:2:end), PQ(2:2:end)))

No matter what you do, you will need a way to identify the Ps from the Qs in order to calculate your S. In the above I assume they alternate. If they don't, you'll have to create two different A matrices.