# [gmx-users] g_anaeig

Berk Hess gmx3 at hotmail.com
Mon Aug 9 12:49:00 CEST 2004

```>What I would really like to do now is generate a single matrix of
>structures as follows
>
>Structure(x,y)=average structure + (x*eigenvector1) + (y*eigenvector 2)
>
>Where x and y are in the range -2,-1,0,1,2 (or some scaled equivalent).
>Looking at it this way the current output of

I do not think this is what you want.
First you probably want to scale each direction with the square root
of the corresponding eigenvalue.
But the ensemble you create has no resemblance to the real ensemble.

Imagine a two-dimensional system with potential V(x,y) = x^2 + y^2
If you sample this completely you would get two identical eigenvalues.
If you apply what you want, you would create dots on a square grid,
which would suggest that the corners of the square are sampled
more often than the points along the axes at the same distance.
This does not correspond to the real sampling, which only depends
on the distance and not on the angle. The real sampling is:
const*exp(-V(x,y)) = const*exp(-x^2-y^2)

The idea of making such an ensemble is contrary to the idea
of principal components which converts an ensemble to
orthogonal modes.

Note that there is a tool g_nmens that generates a (correct) random
ensemble for normal modes.

Berk.

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