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

**From**: |
Frank Küster |

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

**Date**: |
Fri, 09 Dec 2005 17:44:41 +0100 |

**User-agent**: |
Gnus/5.1007 (Gnus v5.10.7) Emacs/21.4 (gnu/linux) |

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