The ‘lsqcurvefit’ function can fit Z-data to (X,Y)-data generated by ‘meshgrid’. It is not well-documented so you will need to experiment with your objective function. It may be necessary to set ‘TolFun’ and ‘TolX’ to 1E-8 and ‘MaxFunEvals’ and ‘MaxIter’ to higher than the default values, since these functions may more difficult for ‘lsqnonlin’ to fit.
To illustrate:
a = 2.5;
b = 6.6;
x2 = [ [1 : 0.1 : 10]; 2*[1 : 0.1 : 10] ]'
[Xgrid,Ygrid] = meshgrid(x2(:,1), x2(:,2));
midpt = [median(x2(:,1)) median(x2(:,2))];
y3 = exp([-(a.*(Xgrid-midpt(1))/10).^2 + -(b.*(Ygrid-midpt(2))/10).^2]);
Xind = Xgrid-midpt(1);
Yind = Ygrid-midpt(2);
XYmtx = [Xind Yind];
f3 = @(B,XY) exp(-(B(1).*XY(:,1:size(XY,1))/10).^2 -(B(2).*XY(:,size(XY,1)+1:end)/10).^2);
est_b3 = lsqcurvefit(f3, rand(2,1), [Xind Yind], y3)
Somewhat to my surprise, ‘est_b3’ was a precise fit to the parameters with the default options. You will have to experiment with your function and data and generalize my code to match your requirements.
