What is this error and how do I fix it?

% Set actual constant parameters
AD = 1.2;  % Air density
DV = 1.84e-5;  % Dynamic viscosity
p0 = 101320;  % Air pressure
SH = 1.4; % Specific heat of air
PN = 0.7; % Prandtl constant
c0 = 343; % Air velocity

% Create a vector of frequencies from 0 to 7000 Hz with a step of 1 Hz
frequencies = [125, 250, 500, 1000, 2000, 4000];

% Target SAC values for each frequency
target_SAC = [0.117, 0.164, 0.570, 0.948, 0.964, 0.999];

% Define the function to minimize (residuals)
objective_function = @(params) calculate_residuals(params, frequencies, target_SAC, AD, DV, p0, SH, PN, c0);

% Initial guess for parameters
initial_guess = [0.003, 0.003, 10, 1e5]; % Initial values for VL, TL, T, FR

% Set lower and upper bounds for parameters
lb = [0.001, 0.001, 1, 1e-3];
ub = [0.005, 0.005, 20, 1e8];

% Optimize using lsqnonlin
optimized_params = lsqnonlin(objective_function, initial_guess, lb, ub);

Local minimum possible.
lsqnonlin stopped because the size of the current step is less than
the value of the step size tolerance.

% Display optimized values
disp('Optimized Values:');

Optimized Values:

disp(['   VL: ', num2str(optimized_params(1))]);

   VL: 0.0049655

disp(['   TL: ', num2str(optimized_params(2))]);

   TL: 0.0010096

disp(['   T: ', num2str(optimized_params(3))]);

   T: 1.2337

disp(['   FR: ', num2str(optimized_params(4))]);

   FR: 0.095723

% Calculate SAC with the optimized parameters
optimized_SAC = calculate_SAC(optimized_params, frequencies, AD, DV, p0, SH, PN, c0);

% Display SAC values with the optimized parameters
disp('Optimized SAC Values:');

Optimized SAC Values:

disp(['   125 Hz: ', num2str(optimized_SAC(1))]);

   125 Hz: 0.063996

disp(['   250 Hz: ', num2str(optimized_SAC(2))]);

   250 Hz: 0.22146

disp(['   500 Hz: ', num2str(optimized_SAC(3))]);

   500 Hz: 0.57354

disp(['   1000 Hz: ', num2str(optimized_SAC(4))]);

   1000 Hz: 0.92844

disp(['   2000 Hz: ', num2str(optimized_SAC(5))]);

   2000 Hz: 0.94591

disp(['   4000 Hz: ', num2str(optimized_SAC(6))]);

   4000 Hz: 0.97167

function residuals = calculate_residuals(params, frequencies, target_SAC, AD, DV, p0, SH, PN, c0)
% Calculate SAC with given parameters
calculated_SAC = calculate_SAC(params, frequencies, AD, DV, p0, SH, PN, c0);

% Calculate residuals (difference between calculated and target SAC)
residuals = calculated_SAC - target_SAC;
end

function SAC = calculate_SAC(params, frequencies, AD, DV, p0, SH, PN, c0)
% Extract parameters
VL = params(1);
TL = params(2);
T = params(3);
FR = params(4);

% Additional constants
d = 0.060;  % Assuming a constant value for d
P = 0.977;  % Assuming a constant value for P

% Initialize SAC array
SAC = zeros(size(frequencies));

% Loop through different frequencies
for i = 1:numel(frequencies)
    f = frequencies(i);
    
    % Evaluate equations for the current set of parameters
    E3 = sqrt(1 + (4 * 1i * T * T * DV * 2 * pi * f * AD) / (FR * FR * VL * VL * p0 * p0));
    E4 = FR * p0 ./ (1i * 2 * pi * f * AD * T);
    E1 = T * AD .* (1 + E4 .* E3);
    E6 = 1i * 8 * 2 * pi * f ./ (PN * AD * 2 * pi * f * TL * TL);
    E7 = sqrt(1 + (1i * PN * AD * 2 * pi * f * TL * TL / 16 * DV));
    E8 = 1./(1 - (E6 .* E7));
    E2 = (SH * p0) ./ (SH - ((SH - 1).* E8));
    KC = 2 * pi * f .* sqrt(E1 ./ E2);
    ZC = sqrt(E1 .* E2);
    ZS = -1i * ZC .* cot(KC .* d) / P;
    R = (ZS - AD * c0) ./ (ZS + AD * c0);
    SAC(i) = 1 - abs(R).^2;
end
end

Unrecognized function or variable 'calculate_residuals'.

Error in @(params)calculate_residuals(params,frequencies,target_SAC,AD,DV,p0,SH,PN,c0)

Error in lsqnonlin (line 242)

initVals.F = feval(funfcn{3},xCurrent,varargin{:});

[Dyuman Joshi]

The code seems to be working here without any errors, see the edit above.

[Pramodya]

Thank you very much for providing a solution. However, it gives the below error. Do I need to download additional plugins as this errors is appearing.

Unrecognized function or variable 'calculate_residuals'.

Error in @(params)calculate_residuals(params,frequencies,target_SAC,AD,DV,p0,SH,PN,c0)

Error in lsqnonlin (line 242)

initVals.F = feval(funfcn{3},xCurrent,varargin{:});

Answer 1

[Dyuman Joshi]

Most likely the function "calculate_residuals" is not in the current directory.

Type "cd" in the command window to get the current directory, check whether the function is present there or not. Check for "calculate_SAC" as well.

If they are not present there, you should move them to the current directory or add them to the current path.

[Pramodya]

Thank you very much. It worked!! Followed the instructions and saved all files in the current directory. Thank you again!A great support!

[Dyuman Joshi]

@Pramodya - You're welcome!

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