fit multiple gaussian surface peaks in matlab

main.m
% Define the surface data (replace with your own data)
x = 1:100;
y = 1:100;
[X, Y] = meshgrid(x, y);
Z = 2*exp(-((X-30).^2 + (Y-70).^2)/50^2) + ...
    1.5*exp(-((X-70).^2 + (Y-40).^2)/30^2) + ...
    3*exp(-((X-50).^2 + (Y-80).^2)/40^2) + ...
    randn(size(X))*0.2;

% Define the number of Gaussian peaks you want to fit
nPeaks = 3;

% Define initial guesses for peak parameters
initialParams = [];
for i = 1:nPeaks
    initialParams = [initialParams, [max(Z(:)), mean(x), std(x), max(Z(:))/10]];
end

% Define the function to fit (sum of Gaussian peaks)
gaussianPeak = @(params, xy) sum(params(1:nPeaks) .* ...
    exp(-(xy(:,1) - params(nPeaks+1:2*nPeaks)).^2 ./ ...
    (2*params(2*nPeaks+1:3*nPeaks).^2)));

% Perform the fitting using lsqcurvefit
fitParams = lsqcurvefit(gaussianPeak, initialParams, [X(:), Y(:)], Z(:));

% Evaluate the fitted function
fittedZ = reshape(gaussianPeak(fitParams, [X(:), Y(:)]), size(X));

% Plot the original and fitted surface data
figure;
subplot(1, 2, 1);
surf(X, Y, Z);
title('Original Data');
subplot(1, 2, 2);
surf(X, Y, fittedZ);
title('Fitted Data');
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