MATLAB: Curve fitting with lsqcurvefit (2 curves simultaneously)

curve fittinglsqcurvefit

Hello.

I need to adjust a few parameters x1, x2, .., xn of two different functions f1 and f2 simultaneously to some experimental data. When using lsqcurvefit, I can only fit parameters of a single function. I've actually solved my problem by creating a function f = f1+f2 and adjusting the parameters so f fits the sum of the points obtained experimentally for each function. I think there might be a better way to do that, since my results aren't good yet. What would you suggest? I've also tried to use fminsearch to minimize the residual using the least squares method, but it didn't work.

Thanks in advance.

Best Answer

When using lsqcurvefit, I can only fit parameters of a single function.

Why? You do know that the output of F(x,xdata) can be vector/matrix valued, right? The only requirement from the documentation is

"ydata must be the same size as the vector (or matrix) F returned by fun."

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MATLAB: Matlab curve fitting tool automation for selection of fit with minimum sse.

You could certainly write your own function by using the gof output of the "fit" function.

Here is an example that shows you how to use the "fit" to see the Goodness of Fit of different methods. You could store the "gof" values in an array and find the max GoF.

function bestFitName = Gof_Finder( x, y )
    Fits = {'poly1', 'poly2', 'poly3', 'exp1'};
      for i=1:numel(Fits)
          [~,GoFs(i)] = fit( x, y,  Fits{i} );
      end
      [~, minIdx] = min([GoFs.sse]);
      bestFitName = Fits{minIdx};
  end

The above function will return the name of the best fit of the data x and y.

MATLAB: Fitting multiple datasets simultaneously

I don't know what that function is. But why not just do it in code with the polyfit() function? Just stitch together the multiple x and y before passing in

coefficients = polyfit(multipleXs, multipleYs, 1);

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MATLAB: Matlab curve fitting tool automation for selection of fit with minimum sse.

MATLAB: Fitting multiple datasets simultaneously

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