Re: [Help-gsl] least-squares fitting or minimization with constrained parameters

[Frank Küster]

address@hidden wrote:

> Hi Frank,
> let me try to give you a general answer which has nothing to do with GSL
> library. The better, safest and probably faster way of introducing the
> kind of constraints you mention is through a re-parameterization of the
> problem. For instance, if you want to fit the sum of two exponentials
>
> a_1*exp{-b_1 t} + a_2 * exp{-b_2 t}
>
> with b_2>b_1>0 and a_1,a_2>0 rewrite the function as
>
> exp(-d_1^2 t+c_1) *(1.+exp(-d_2^2 t +c_2))

That sounds reasonable, however it has a practical disadvantage: I have
to change the fitted function and the parameter set every time I want to
try a new type of constraints.  I have not yet really thought about how
I would let the user set the fitted function at runtime (any hints
appreciated), but recompiling just to set a constraint would be
tedious... 

> Said that, some time ago I wrote a "wrapper" function around GSL
> minimization functions which implements BOUNDARIES constraints through
> change of variable approach. I use it for max-likelihood fitting and
> it seems to work. If you still need it, just ask.

I'd like to have a look at this, yes.  

Thank you, Frank
-- 
Frank Küster
Inst. f. Biochemie der Univ. Zürich
Debian Developer