Curvefitting a given function with parameters to pass through given points

I need to curve fit a given data with a function which contains a few parameters. I need to find the values of those parameters. But I need the curve to pass through certain given points too. How do I do this

[Birdman]

Can you share your given data and your function?

[AAKILA RAJAN]

Sorry, but the data is confidential

Answer 1

[Torsten]

Each prescribed point on the curve gives you a relation between the parameters to be estimated. These relations are constraints for the curve fitting process. You can use MATLAB's "fmincon" together with the "nonlcon" function for nonlinear constraints or the Aeq,beq arrays for linear constraints.

Best wishes

Torsten.

[AAKILA RAJAN]

Thanks for the reply. How can I use fmincon if I want the value of the final output of the function being curve fitted to have a specified value.

[Torsten]

Example:

If

p(x)=a*x^2+b*x+c+d*exp(e*x)

is the form of the fitting function and you want to have p(xend) to have a specified value yend, you get the constraint

yend - (a*xend^2+b*xend+c+d*exp(e*xend)) = 0

This constraint has to be implemented in fmincon's "nonlcon" as

ceq(1) = yend - (p(1)*xend^2+p(2)*xend+p(3)+p(4)*exp(p(5)*xend))

And the objective function for the problem is the sum of squared differences between measured and fitted data.

Best wishes

Torsten.

[AAKILA RAJAN]

Thanks a lot. I got it.