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

You're probably not going to find a single routine with the flexibility implied in your examples (polynomials and rational functions using the same routine), let alone one that will parse a string to figure out what sort of equation to fit.

A least-squares polynomial fitter would be appropriate for your first example. (It's up to you what degree polynomial to use -- quadradic, cubic, quartic, etc.). For a rational function like your second example, you might have to "roll your own" if you can't find a suitable library. Also, keep in mind that a sufficiently high-degree polynomial can be used to approximate your "real" function, as long as you don't need to extrapolate beyond the limits of the data set you're fitting to.

As others have noted, there are other, more generalized parameter estimation algorithms which might also prove useful. But those algorithms aren't quite "plug and play": they usually require you to write some helper routines, and supply a list of initial values for the model parameters. It's possible for these sorts of algorithms to diverge, or get stuck in a local minimum or maximum for an unlucky choice of initial parameter estimates.