Finding a curve to match data

Question

I\'m looking for a non-linear curve fitting routine (probably most likely to be found in R or Python, but I\'m open to other languages) which would take x,y data and fit a c

Answer 1

if you have constraints on your coefficients, and you know that there is a specific type of function you'd want to fit to your data and that function is a messy one where standard regression methods or other curve fitting methods won't work, have you considered genetic algorithms?

they're not my first choice, but if you are trying to find the coefficients of the second function you mentioned, then perhaps GAs would work --- especially if you are using non-standard metrics to evaluate best fit. for example, if you wanted to find the coefficients of "(A+Bx+Cx^2)/(Dx+Ex^2)" such that the sum of square differences between your function and data is minimal and that there be some constraint on the arclength of the resulting function, then a stochastic algorithm might be a good way to approach this.

some caveats: 1) stochastic algorithms won't guarantee the best solution, but they will often be very close. 2) you have to be careful about the stability of the algorithm.

on a longer note, if you are at the stage where you want to find a function from some space of functions that best fits your data (e.g., you are not going to impose, say, the second model on your data), then genetic programming techniques may also help.