MATLAB: MATLAB Curve fitting with custom equation

curve fittingCurve Fitting Toolboxcustom fittingexponential equation

Hello,
I have a data (x,y) points and I want to fit it with custom equation as y = a*(1-exp(-b*x))+c*(exp(d*x)-1). I want to get a, b, c, d values after fitting with custom equation.The problem I am facing is that, the curve fitting happens to be good in the initial part of the data points, then at the later points of data, it does not fit properly. How to tweak with fitoptions so that I can fit my data exactly with custom equation. Also, if there needs any change to be done in the script please help me with that too, so that I can fit it exactly. If you can provide me snaps of the script that you are following to fit kindly share that too as it will help me to understand properly.
I am attaching the data file for your reference.
Thank you

Best Answer

If you have the curve fitting toolbox, I suggest using fittype and fit.
fittype will allow you to define a custom equation to fit to your data, and fit will try to fit that equation to your data. Just a caution, your model is much more complex than your data requires. This means you will need to provide reasonable estimates for your initial guesses (StartPoint) for coefficients a-d.
You can find a good example here.
data=readtable("675_base.xlsx");
ft = fittype('a*(1-exp(-b*x))+c*(exp(d*x)-1)',...
    'dependent',{'y'},'independent',{'x'},...
    'coefficients',{'a','b','c','d'});
f = fit(data.x,data.y,ft,'StartPoint',[0,0,0,0.25])
f = 
     General model:
     f(x) = a*(1-exp(-b*x))+c*(exp(d*x)-1)
     Coefficients (with 95% confidence bounds):
       a =           0
       b =           0
       c =   0.0006586  (0.0006251, 0.0006921)
       d =      0.0946  (0.09362, 0.09558)
plot(f,data.x,data.y)
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