[AstroPy] non-linear least square fitting in python

[Aldcroft, Thomas]

On Thu, May 14, 2015 at 5:52 AM, gonghang.naoc <ghang.naoc at gmail.com> wrote:

> Hi all,
> We can use scipy.optimize.leastsq to do least square fitting in python.
> However we need to make an initial guess. (
> http://python4mpia.github.io/fitting_data/least-squares-fitting.html). So
> I am not sure we can get a global optimum.
>

Ensuring that you have a global optimum for a non-linear is generally a
difficult problem.  In your case though you have a reasonably simple fit
function so that if you provide a decent initial guess then most optimizers
should converge to something near the global optimum.

You can make an initial guess in your case by taking 3 data points, at the
beginning, middle, and end of your data.  With those three data points you
can analytically solve for a, b, and c.  Then use those as the starting
point.  If your data are very noisy you might average a few.

Cheers,
Tom


>
> There is other simple way we can fit a *y=a*e^-(b*x)+c* curve? My data
> are  Xn, Yn and ERRORn. A constant c makes the fitting difficult since we
> can not make a log on both sides and use linear fitting any more.
>
> Thank you.
> best
> Hang
>
>
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