how i can find this in MATLAB in order to find (τ,ν): I want the code and i will fix it

(τ,ν)= argmax(τ,ν) ​xp^H ​A(τ,ν) (A(τ,ν)^H A(τ,ν))−1 A(τ,ν)H xp

how i can find this in matlab

note: all coefficients are vector

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[Torsten]

xp is a given vector ? A is a matrix with elements depending nonlinearly on tau and nu ?

A few more explanations may help to get a useful answer.

Answer 1

[Aastha]

Hi shadi,

I understand that you are looking to find the values of “tau” and “v” that maximize the given expression. Assuming you have a function that computes the matrix “A” using “tau” and “v” as inputs, you can kindly follow the steps mentioned below to find the optimal values:

1) First, set a range of values for “tau” and “v” to define your search space. Then, you can create a matrix containing indices referring to the “tau_range” and “v_range”, representing possible values for “tau” and “v”. You can do this using the "meshgrid" function in MATLAB as follows:

tau_range; 
v_range; 
[tau_idx, v_idx] = meshgrid(1:length(tau_range), 1:length(v_range)); 
search_space = [tau_idx(:), v_idx(:)]; 

You may find the link to the documentation of “meshgrid” function below:

https://www.mathworks.com/help/matlab/ref/meshgrid.html

2) Next, you can iterate over the search space using a for-loop to compute the value of the expression. After that, you can identify the maximum value and store the corresponding indices as shown below:

max_idx = -1; 
max_expression = 0; 
for i = 1:size(search_space, 1) 
    A_tau_v = A(tau_range(search_space(i, 1)), v_range(search_space(i, 2))); 
    expression = xp' * (A_tau_v)' * inv(A_tau_v' * A_tau_v) * A_tau_v' * xp; 
    
    if i == 1 
        max_idx = 1; 
        max_expression = expression; 
    else 
        if expression > max_expression 
            max_idx = i; 
            max_expression = expression; 
        end 
    end 
end 
 
disp("Best tau is: "); 
disp(num2str(tau_range(search_space(max_idx, 1)))); 
disp("Best v is: "); 
disp(num2str(v_range(search_space(max_idx, 2)))); 

This method will allow you to find the optimal values for “tau” and “v”.

Hope this helps!