When I am fiiting my experimental data clicking exponetial fit, then it fits well. But when I am writing the same equation in customised form its not fitting.
MATLAB: Exponential fit by customised equation
customised equationexponential equationgoodness of fitmatalb 2018b
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There are a plethora of issues that influence curve fitting.
1. The most notable is selection of model, either from our curve-fitting library or the user's custom equations. We suggest trying different models to fit the data.
2. Some preprocessing of data prior to fitting curve is helpful. This may include:
- Transforming the response data.
- Removing Infs, NaNs, and outliers.
3. The fitting process is more likely to converge if you supply as much information as possible about the coefficients being estimated:
- Make intelligent guesses as starting values. If you have an idea about the likely coefficient values, then use those as starting values.
- In absence of knowledge of starting values, try a variety of different starting values.
- Try restraining the parameters. For example if you know a parameter has to be positive, placing its lower bound at 0 may lead the iterative process toward a solution that it might not find otherwise.
4. There are various fitting options that you can adjust:
- Try different algorithms.
- Increase the number of iterations or function evaluations allowed.
- Reduce the convergence tolerance.
5. Try also sub-setting the data and fitting different subsets of data separately.
6. Another strategy is to fit a term at a time. So say you think your model is
y = c+ a*exp(b*x) + d*sin(f*x);Then you might want to fit
y = c + a*exp(b*x)and then use the resulting coefficients for a, b, and c as starting points when fitting the whole equation
y = c+ a*exp(b*x) + d*sin(f*x);Using the 'power1' fit type, I obtain pretty close agreement.
>> cfit = fit(x1(x1>0),y1(x1>0),'power1')cfit = General model Power1: cfit(x) = a*x^b Coefficients (with 95% confidence bounds):
a = -0.07755 (-0.07888, -0.07622) b = 3.316 (3.312, 3.32) >> plot(cfit,x1,y1)
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