How do I find the find the maximum value of absolute of a complex function ?

I have a complex function which takes real numbers as input. Now I need to take it's modulus and find the maximum of this modulus ? How do I do this ?

Now how do we find the K at which abs(G) obtains it's maxima. Also what is the value of this maxima ?

For this example, I have taken an arbitrary value of s. Actually I need to keep varying s and find the K at which the absolute value is maximum. How do I code this in MATLAB ?

Answer 1

[Lokesh]

Hi Sahil,

As per my understanding, you have a complex function that accepts real numbers as input, and you wish to find the maximum value and value of the variable at which the modulus of function is maximized. To do this, you can follow these general steps:

• Define the function in terms of the variable.
• Compute the modulus of the function.
• Optimize the modulus to find the maximum value and the corresponding variable.

To solve this problem in MATLAB, you can define the complex function as a function handle, compute the modulus using 'abs' function and then use optimization function 'fminbnd' to find the maximum modulus and the value of variable at which the modulus is maximum. Since 'fminbnd' finds minima, you can minimize the negative modulus to find the maximum.

Below is an example code snippet for a sample complex function:

% Define the complex function G as a function of K
s = 1;
G = @(K) (K + 1i*s)^2; % Replace with your actual function

% Define a function to return the negative modulus of G
% We use negative because optimization functions typically minimize
modulus_function = @(K) -abs(G(K));

% Set the range for K if it is known
% Note: The range (Kmin, Kmax) is % exclusive
Kmin = 0; % Replace with the minimum value of K
Kmax = 10; % Replace with the maximum value of K

% Find the value of K that minimizes the negative modulus, which is equivalent
% to maximizing the modulus
[K_opt, max_modulus_neg] = fminbnd(modulus_function, Kmin, Kmax);

% Since we minimized the negative modulus, take the negative of the output to get the max modulus
max_modulus = -max_modulus_neg;

% Display the results
fprintf('The maximum modulus of G is %f and occurs at K = %f\n', max_modulus, K_opt);

Please refer to the following MathWorks documentation to know more about ‘fminbnd’ :

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