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Re: [Help-gsl] constraints over variables?

From: Claudio Ochoa
Subject: Re: [Help-gsl] constraints over variables?
Date: Tue, 22 May 2007 09:36:19 -0300
User-agent: Thunderbird (X11/20070306)


John Gehman wrote:
> Depending on the transformation matrix and the noise in the information
> that you're trying to fit, you may need to reset some of your singular
> values to zero -- if you plot out your singular values, (they come out
> in rank order, I believe), you may find a obvious discontinuity, and
> therefore an obvious value below which the singular values become
> insignificant and only cripple your floating variables with noise, which
> might be why some of them turn out inappropriate? 

Basically I have a lot of noise. I have some input data, let
us say 15 equations, 5 variables, and removing some of the
equations leads to completely different values. The ideal
case would be to take, for instance, 12 out of the 15
equations, and the interchange of some of the 12 for some
other equations do not affecting the obtained values, but
this is not the case. As I said, I am pretty new to both gsl
and this kind of problems, so any pointers to articles on
the web will be greatly appreciated. Also, could you tell me
how can I reset the singular values to zero as you suggest?

> Otherwise, you could try a straightforward nonlinear least squares
> approach? If it's too difficult to choose an appropriate starting
> configuration for your variables, maybe use a quick simulated annealing
> to find a reasonable starting configuration, then proceed with usual
> nonlinear least squares.

I can try this, I read the documentation in chapter 37 of
gsl but this is not enough, since I don't know how to map
this into my problem. But your hint of simulated annealing
can help. Thanks

> Also, you could think about working instead with an objective function
> which incorporates your constraints as lagrange multipliers, and
> optimise it instead.
> These are blind thoughts, of course, without being as familiar as you
> are about what you're after, but maybe it helps?

Yes, they help a lot. I will analyze them and see if I can
do anything. Thanks a lot!!

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