Can someone explain this?

Hi everyone,

Something strange is happening in my code and I would like ti figure out. I have a nested loop like this:

sum_F = zeros(2048,188);
% E is a 1x2048 complex vector
for j = 1:188 
    disp(j)
    v = zeros(1,2048);
    for i = 1:2048 
        if find(freqind==i) % condition to reduce the number of points to be calculated
            T = mat_T(nodes_steps(:,:,j), points, ka(i)); % nodes_steps is a 2080x3x188 tensor, points is a 3x3 matrix and k is a complex number
            R = SL2_r(i).*eye(n_r); % diagonal matrix
            R = sparse(R);
            F = T.'*(R*sum(T,2)); %  F is a 2080x1 complex vector
            v(i) = sum(F)*E(i); %<---- case 1. 
            sum_F(i,j) = sum(F)*E(i); %<---- case 2
        end
    end
    sum_FR(:,j) = v'.*exp(1i*2*pi*(frecs')/ct*z0);  % <---- case 1
    sum_FR(:,j) = sum_F(:,j).*exp(1i*2*pi*(frecs')/ct*z0); % <----- case 2
end

At first view everyone should think, as I did, that in both cases the value assignated to sum_FR(:,j) in every j-loop should be the same regardless of the case because in case 1 I am multiplying a column vector by a column vector. And in case 2 I am multiplying the same column vector by the other same column vector, and also v and the columns of matrix sum_F are calculated the same way. But in reality the results obtained in the case 1 are simetrics with obtained in case 2. As shown in the pictures:

Case 1

Case 2

When I realized this I started to investigate to see what was going on. And I found out that the norm between v' and sum_FR(:,j) is not 0 but 0.0333 and to me it doesn't make any sense because they should be the same vector. If I declare v as a column vector the norm between both vectors is now 0 as it should be. Can someone explain me what is happening? Why when I transpose the vector their values vary? Or why it has a different value if I declare it as a row vector or as a column vector?

P.S.: The correct result is the case 2

Thank you all!!

[Alex Bernadí Forteza]

What is happening here is that v is a complex vector so if I perfom v' it results the transposed conjugate vector and that why norm( v' - sum_FR(j:enf)) ~=0. To fix that you just need to calculate the transposed vector using .' instead of '

[Jan]

Correct. Please post this as an answer, such that it can be selected as a solution.

Answer 1

[Alex Bernadí Forteza]

What is happening here is that v is a complex vector so if I perfom v' it results the transposed conjugate vector and that why norm( v' - sum_FR(j:enf)) ~=0. To fix that you just need to calculate the transposed vector using .' instead of '