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

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shadi
shadi 2024-2-5
回答： Aastha 2024-10-5
(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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  1 个评论
Torsten
Torsten 2024-2-5
编辑：Torsten 2024-2-5
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.

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回答（1 个）

Aastha
Aastha 2024-10-5
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!

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