Least square fitting of experimental data

I have experimantal data xdata,ydata; and I want to fit a model to these data, the model shape is like Y(xdata)=[A*exp(C*D/xdata)]/[E+F*exp(C*D/xdata)+...]; where Y should be very near to ydata (curve fitting), my problem is that the parameters A B C D... are function of xdata too with sub-parameters to be determined, I proceeded to write a huge function of sub-parameters but the process takes time of writing code and checking and if there is error it is difficult to locate it, so my question is : can I declare these parameters as parametric variables and how to do it if possible? and; is there other shortcut to bypass the long functions which increase the possibility of typing errors and facilitate the replacement of the variable function like I input A=exp(a-c); and if does not give good results I change easily to A=(1/d+e)?... thanks in advance

Answer 1

[Alan Weiss]

If you have Symbolic Math Toolbox, you can use matlabFunction to generate your function handles or program files. For examples related to optimization (not exactly curve fitting, but close, you would use lsqnonlin or lsqcurvefit instead of fmincon), see this example or this example. There is also an example on the file exchange that uses data in a symbolic test, and might be somewhat relevant.

Alan Weiss

MATLAB mathematical toolbox documentation

[Zine]

Thanks Alan for the very useful information that you gave me which is exactely what I have in mind, I am sorry to say that it solved half of my problem which is writing symbolic variables, but when it comes to do the numerical evaluation I could not tell MATLAB how to assign values to these variables since I want to use these symbolic expressions to declare the variables and then convert them into normal variables for the rest of program, note I am using non linear least square curve fitting with constraines

[Alan Weiss]

Did you look at the use of matlabFunction in the examples I linked? It converts symbolic variables to function handles or MATLAB files that then use numeric variables.

Alan Weiss

MATLAB mathematical toolbox documentation

[Zine]

thanks very much, solved

Answer 2

[John D'Errico]

This just seems a problem of modular programming. It means you need to learn a good programming style, so that you CAN modify component parts of your function. But there is very little we can do for you in that respect.

• Break the problem into pieces.
• Learn to use nested functions.
• Test every piece separately. If they all work separately, then they will work as a whole.
• Document your code, so it will be easy to debug. If the code is easy to read, it will be easy to repair too.

Beyond that, there is no magic. There are no shortcuts to writing good code.