# [gmx-users] g_covar -ref

vijaya subramanian vijaya65 at hotmail.com
Thu Mar 18 19:01:48 CET 2010

```PCA refers to covariance analysis (though SVD gives the same results).
Principal components are obtained by projecting the trajectory onto
the eigenvectors of the covariance matrix.
I just wanted to know why the option -ref was offered and if it had any significance.
Thanks
Vijaya

> Date: Thu, 18 Mar 2010 17:51:04 +0100
> Subject: Re: [gmx-users] g_covar -ref
> From: tsjerkw at gmail.com
> To: gmx-users at gromacs.org
>
> Hi Vijaya,
>
> Well, to start with that will be something as calculating the
> 'fluctuation' as sum((xi-ri)^2)/N, with xi and ri denoting the ith
> atom of the conformation x and the reference structure r and the sum
> is over time/observations. In the case of no variation in xi, the
> value you get will still be finite, in stead of zero, as would
> probably be most meaningful.
> Now for the covariances, there's a bit more to it. The covariance is
> the product moment of the deviations: sum((xi-ri)(xj-rj))/N. When
> there is no correlation, the deviations about the mean are random and
> average out to zero. But with the deviations against a reference, that
> is not the case. So the results should be regarded meaningless, unless
> you have a good reason for doing so, and come with a solid
> justification. Okay, there may be a purpose, but I'll leave that to
>
> Hope it helps,
>
> Tsjerk
>
> On Thu, Mar 18, 2010 at 5:33 PM, vijaya subramanian
> <vijaya65 at hotmail.com> wrote:
> > Hi
> > Has anyone studied the effect of using different reference structures,
> > not the average structure, when carrying out PCA.  Does it make sense to use
> > a structure besides the average to calculate the covariance matrix?
> > Thanks
> > Vijaya
> >
> >
> >
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>
>
> --
> Tsjerk A. Wassenaar, Ph.D.
>
> post-doctoral researcher
> Molecular Dynamics Group
> Groningen Institute for Biomolecular Research and Biotechnology
> University of Groningen
> The Netherlands
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