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Re: Leasqr matrix singular to machine precision

From: Dmitri A. Sergatskov
Subject: Re: Leasqr matrix singular to machine precision
Date: Mon, 25 Feb 2008 19:40:14 -0600

On Mon, Feb 25, 2008 at 3:26 PM, Archambault Fabien
<address@hidden> wrote:
> Przemek Klosowski a écrit :
>  >    For the weight on some points I thought of it but as the values I get
>  >    are all of the same importance I think fitting with wt = (1) is a
>  >    correct guess.
>  >
>  > I would caution against it---every target point has its own
>  > experimental, or systematic, or other kind of error, and those errors
>  > are rarely the same for all points. For instance, if the points were
>  > calculated in a counting experiment, i.e. they represent counts per
>  > some unit of time, or are a result of a monte carlo simulation, their
>  > error will likely be proportional to the square root of the value.
>  >
>  >
>  >       p
>  >
>  >
>  Hi,
>  no values that are fitted are not from experimental values they are from
>  QM calculations so each points are the "truth" (compared with MM values).
>  In the last tests I made it was still impossible to achieve on 4 (or 6
>  unknown). Also the lmder (in Fortran) did not work well... And since
>  today I tried to solve it with the nonlinear fitting of Xmgrace
>  (constrained values are possible) and it is still not very good in fit.
>  Still working on it but few hope (lol).

All this should give you a clue that you are doing something wrong.
In fact your equation has only 4 independent variables (I re-wrote it
for clarity):

Y = A*( ((x1/r1)^12 -(x1/r1)^6) + ((x1/r2)^12 -(x1/r2)^6) +
        B*((x2/r3)^12 - (x2/r3)^6) )

So the parameters here is A, B, x1 and x2.

Fitting this with 6 parameters will not work.
>  --
>  Fabien Archambault


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