How do I calculate result for every value in a matrix in MATLAB

Question

Keeping simple, take a matrix of ones i.e.

U_iso = ones(72,37)

and some parameters

ThDeg = 0:5:180;
dtheta = 5*pi/180;
dphi = 5*pi/180;
Th = ThDeg*pi/180;

Now the code is

omega_iso = 0;
for i = 1:72
    for j=1:37
        omega_iso = omega_iso + U_iso(i,j)*sin(Th(j))*dphi*dtheta;
    end
end

and

D_iso = (4 * pi)/omega_iso

This code is fine. It take a matrix with dimension 72*37. The loop is an approximation of the integral which is further divided by 4pi to get ONE value of directivity of antenna.

Now this code gives one value which will be around 1.002.

My problem is I dont need 1 value. I need a 72*37 matrix as my answer where the above integral approximation is implemented on each cell of the 72 * 37 matrix. and thus the Directviity 'D' also results in a matrix of same size with each cell giving the same value.

So all we have to do is instead of getting 1 value, we need value at each cell.

Can anyone please help.

Answer 1

You talk about creating a result that is a function essentially of the elements of U. However, in no place is that code dependent on the elements of U. Look carefully at what you have written. While you do use the variable U_iso, never is any element of U employed anywhere in that code as you have written it.

So while you talk about defining this for a matrix U, that definition is meaningless. So far, it appears that a call to repmat at the very end would create a matrix of the desired size, and clearly that is not what you are looking for.

Perhaps you tried to make the problem simple for ease of explanation. But what you did was to over-simplify, not leaving us with something that even made any sense. Please explain your problem more clearly and show code that is consistent with your explanation, for a better answer than I can provide so far.

(Note: One option MIGHT be to use arrayfun. Or the answer to this question might be more trivial, using simple vectorized operations. I cannot know at this point.)

EDIT:

Your question is still unanswerable. This loop creates a single scalar result, essentially summing over the entire array. You don't say what you mean for the integral to be computed for each element of U_iso, since you are already summing over the entire array. Please learn to be accurate in your questions, otherwise we are just guessing as to what you mean.

My best guess at the moment is that you might wish to compute a cumulative integral, in two dimensions. cumtrapz can help you there, IF that is your goal. But I'm not sure it is your goal, since your explanation is so incomplete.

You say that you wish to get the same value in each cell of the result. If that is what you wish, then a call to repmat at the end will do what you wish.