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

From: g1ul10
Subject: Re: [Help-gsl] least-squares fitting or minimization with constrained parameters
Date: Fri, 9 Dec 2005 16:37:18 +0100

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))

and fit c_1,c_2,d_1,d_2. When you have the fit, compute the old
variables as


and use the rules of propagation of errors to find the new error

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.

Hope this could help,

On Fri, 09 Dec 2005 10:04:14 +0100
Frank Küster <address@hidden> wrote:

> Hi,
> I am wondering whether (and how) it is possible to use the least-squares
> fitting, or alternatively minimization functions of gsl with constrained
> parameters.  What I mean with this is that I want to force the function
> into the correct local minimum by supplying information which parameter
> values are physically meaningful for these particular data, or which of
> two degenerate minima I would like (to be able to compare different
> fits).  For example, if the function is the sum of two exponentials, I
> would like to perform a least-squares fit to some data with the
> constrain that the first of them has the shorter relaxation time.
> Is this possible, and how would that be implemented?
> TIA, Frank
> -- 
> Frank Küster
> Inst. f. Biochemie der Univ. Zürich
> Debian Developer
> _______________________________________________
> Help-gsl mailing list
> address@hidden

Giulio Bottazzi                 PGP Key ID:BAB0A33F 

CAFiM  Center for the Analysis of Financial Markets
LEM          Laboratory of Economics and Management
Sant'Anna School for Advanced Studies, Pisa, Italy
Phone: (+39)-050-883365       Fax: (+39)-050-883344
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