matlab simultaneous fitting of exponential to surface in matlab

main.m
function y = exponentialSurfaceModel(x, params)
% x: input variables (e.g., x and y coordinates)
% params: parameters of the surface model

% Extract parameters
a = params(1);
b = params(2);
c = params(3);

% Calculate the surface using the exponential equation
y = a * exp(-b * x(:,1)) .* exp(-c * x(:,2));
end
312 chars
13 lines

main.m
% Generate input data
x1 = linspace(0, 1, 100);
x2 = linspace(0, 1, 100);
[X1, X2] = meshgrid(x1, x2);
x = [X1(:), X2(:)];

% Set true parameters for the surface model
trueParams = [2, 3, 4];

% Generate surface data based on the true parameters
yTrue = exponentialSurfaceModel(x, trueParams);

% Add noise to the surface data
noiseStd = 0.1; % standard deviation of the noise
yNoisy = yTrue + noiseStd * randn(size(yTrue));
425 chars
16 lines

main.m
function residuals = exponentialSurfaceResiduals(params, x, yObserved)
% params: parameters of the surface model
% x: input variables
% yObserved: observed data

% Calculate the predictions of the model
yPredicted = exponentialSurfaceModel(x, params);

% Calculate the residuals
residuals = yPredicted - yObserved;
end
319 chars
12 lines

main.m
% Initial guess for the parameters
initialParams = [1, 1, 1]; % adjust according to your data

% Run the simultaneous fitting
paramsEst = lsqcurvefit(@exponentialSurfaceModel, initialParams, x, yNoisy, [], [], options);
220 chars
6 lines