How do I best fit a function's parameters to a curve

[rsr_life]

Hello,

Suppose,
1. I have a function f=C1 + C2/((C3-X)^C4); where Cn is a constant;
I'm looking at the Havriliak-Negami equation which has some 5 constants.

2. I have a data set whose least-squares fit looks like a curve,

How can I compute the values of the function's parameters C1 to C4 that would best fit this function 1 to the curve?

One idea I had was to do a separate curve fitting for the data set (using a polynomial or a set of gaussians), then take the Fourier series of that resulting fitting function; compare those terms to the Fourier series of this function f, and solve any resulting equations containing C1 to C4.

But I bet there's some Matlab function that does this job better if I simply supply the data set and the function? i.e. it optimizes the functions parameters to get me the best least squares fit to the data set?

Any help with Matlab or pointers to this is appreciated!

Many thanks.

 

[Simon Bridge]

I have a data set whose least-squares fit looks like a curve.

"least squares fit" to which curve?

http://www.mathworks.com/help/optim/ug/lsqnonlin.html
http://www.mathworks.com/moler/leastsquares.pdf

 

[rsr_life]

Ok. A fit of the function I described to any curve that would best cover the data set I have.

The data set, when plotted, looks like a half ellipse (and is independent of the function).

I need to find the values of the the function's parameters C1 to C4 that would best fit this curve. There are other functions too that could describe this dataset, but I need to compute how I could specifically use this function to describe them.

Thank you!

 

[Simon Bridge]

Those links I gave you should help with what you want.

 

[alphy]

Hello,

Thank you for your question. Fitting a function's parameters to a curve is a common task in scientific research and can be approached in several ways. One approach is to use a least-squares fitting method, which minimizes the sum of the squared differences between the data points and the curve. This can be done using various software packages, including Matlab, by providing the data set and the function to be fitted.

In your case, where you have a function with 5 constants, you can use Matlab's "lsqcurvefit" function. This function allows you to specify a function, initial parameter values, and a data set, and it will return the optimized parameter values that best fit the data to the given function. You can also specify bounds for the parameters to ensure that they fall within a certain range.

Alternatively, as you mentioned, you can also use a polynomial or Gaussian curve fitting method to fit the data, and then use the resulting coefficients as initial values for the constants in your function. This approach may work well if the data can be approximated well by a polynomial or Gaussian function.

In any case, it is important to keep in mind that the accuracy of the fit will depend on the quality and quantity of the data points, as well as the complexity of the function being fitted. It may be helpful to plot the fitted curve alongside the original data to visually assess the fit and make any necessary adjustments.

I hope this helps. Best of luck with your research!