Suppose we have three 10x10 complex matrices and the following equation: R = T * X. Here T is a given fixed matrix.
Now, we want to find the optimized R (I'll explain what "optimized" means) by modifying X. We need to fill X with given four different elements such that at the end we obtain the matrix R which satisfies: abs(R(5,5)).^2 = maximum and other elements of abs(R ).^2 are as minimum as possible. So, this is actually related to obtaining a focus at a given target point (5,5) at the end.
What I tried initially was to choose X = ones(10,10) and then I changed every index of X with 4 given elements, do the multiplication T * X for every 4 elements separately and calculate abs(R(5,5)).^2 for each of them. Then I've chosen the single number inside of these 4 that gives the maximum value for abs(R(5,5)).^2. Repeating that for every index of X, I hoped to find the optimized pattern but I failed.
In my second try, inside a loop I created random X matrices with the given 4 elements and do the calculation T*X for every random X with the condition max(max(abs(R ).^2)) = abs(R(5,5)).^2. But, this code is also not working perfectly. It is taking too much time and I'm not able to find a good looking focused point at (5,5).
So, I need your help in approaching this problem. How should I proceed?
