Re: [Help-gsl] fitting convergence

[John Gehman]

Assuming your initial values for your floating parameters are  
reasonable, perhaps double check the partial derivatives with respect  
to each of those parameters -- that's where I usually slip up.

For your function, I get

partial(y)/partial(Ai) = ( 1 - exp(-x/ti) )
partial(y)/partial(ti) = -Ai*x*exp(-x/ti) / ti^2
partial(y)/partial(Ap) = ( 1 - exp(-x/tp) )
partial(y)/partial(tp) = -Ap*x*exp(-x/tp) / tp^2

without trying them I don't guarantee that they're correct (as I  
said, that's usually where I slip up), but perhaps this will point  
you in the right direction. The signs of the second and fourth  
partial derivatives are tedious, and a likely source of error.  
Obviously you have to adapt this notation into your Fit_df function,  
making sure to order the partials' indices according to the order of  
the parameters in the vector of floats.

Good Luck
john

---------------------------------------------------------

Dr John Gehman (address@hidden)
Research Fellow; Separovic Lab
School of Chemistry
University of Melbourne (Australia)


On 06/09/2006, at 1:06 AM, Petr Ent wrote:

> hello,
> I would like to fit data to following equation using non-lineat  
> least squares fitting. I am using real life data (not generated  
> from equation), but I have pretty good idea about final results and  
> I use it as seed values (starting values which you provide to the  
> solver). but whatever I do, solver does not converge.
>
> equation:
> y = fo + Ai * ( 1 - exp(-x/ti) ) + Ap * ( 1 - exp(-x/tp) )
>
> where Ai, ti, Ap, tp are parameters, fo is constant. shape of the  
> function should be +- logarithmic, parameters should be similar to
> Ai = 800
> ti = 6
> Ap = 200
> tp = 15
>
> I use modified non-linear least squares fitting example.
> I tried to fit same source data using logarithmic and square-root  
> models
> y = a * log (b * x) + c
> y = a * sqrt(b * x) + c
> and both of them converged and results are good.
>
> If anyone has any clue, why the first model does not converge, or  
> what i am doing wrong, I would appreciate it.
> regards Petr Ent
>
> this is method where I use GSL to fitting
>
> const gsl_multifit_fdfsolver_type *T;
> gsl_multifit_fdfsolver *s;
>
> int iter = 0;
>
> gsl_multifit_function_fdf f;
>
> double x_init[maxVars];
> for (unsigned i = 0; i < configData[k].seeds.size(); i++)
> {
>    x_init[i] = configData[k].seeds[i];
> }
>
> gsl_vector_view x = gsl_vector_view_array (x_init,  
> fitData.paramCount);
>
> //Fit_... functions do what they are supposed to do, counting value  
> and derivations
> //fitData is structure with all the info about fitting - data,  
> number of parameters, data length, ...
> f.f = &Fit_f;
> f.df = &Fit_df;
> f.fdf = &Fit_fdf;
> f.n = fitData.n;
> f.p = fitData.paramCount;
> f.params = &fitData;
>
> T = gsl_multifit_fdfsolver_lmsder;
> s = gsl_multifit_fdfsolver_alloc (T, fitData.n, fFunc->paramCount);
>
> gsl_multifit_fdfsolver_set (s, &f, &x.vector);
>
> do
> {
>    iter++;
>    status = gsl_multifit_fdfsolver_iterate (s);
>
>    if (status)
>    {
>       break;
>    }
>    status = gsl_multifit_test_delta (s->dx, s->x,0,1e-2);
> }
> while (status == GSL_CONTINUE && iter < 500);
>
>
>
>
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