fit gaussian with lsqcurvefit in matlab

main.m
function y = gaussian(x, params)
    mu = params(1);
    sigma = params(2);
    A = params(3);
    
    y = A * exp(-(x - mu).^2 / (2 * sigma^2));
end
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main.m
x = linspace(-10, 10, 100);
params_true = [0, 1, 1];  % True parameters: mean, standard deviation, amplitude
y_true = gaussian(x, params_true);
noise = 0.1 * randn(size(x));
y = y_true + noise;
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main.m
function residuals = gaussian_fit(params, x, y)
    predicted_y = gaussian(x, params);
    residuals = y - predicted_y;
end
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main.m
params0 = [0, 1, 1];  % Initial guess for parameters
params_fit = lsqcurvefit(@gaussian, params0, x, y);
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main.m
y_fit = gaussian(x, params_fit);

plot(x, y, 'o', 'DisplayName', 'Data');
hold on;
plot(x, y_true, 'r', 'DisplayName', 'True Gaussian');
plot(x, y_fit, 'g', 'DisplayName', 'Fitted Gaussian');
xlabel('x');
ylabel('y');
legend();
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