[gmx-users] Correlation Matrix Calculation

[Tsjerk Wassenaar]

Hi Arneh,

I think this has been covered on the mailing list before. But anyway,
the number indeed refers to the atom index number, running from 1-N.
You mean that you have 1934427 X 3 elements in the covar.dat file? So
that corresponds to sqrt( 1934427 X 3 ) / 3 = 803 atoms. I think you
made a mistake with the group you chose (Protein rather than
c-alpha?). You would expect to have 90000 elements for a system of 100
atoms.

Hope it helps,

Tsjerk

On 9/5/07, Arneh Babakhani <ababakha at mccammon.ucsd.edu> wrote:
> Thanks Tsjerk,
>
> One other question, regarding the covar.dat file (the covariance matrix
> that's outputted when using the -ascii flag):
>
> I dont' quite understand the format of it.  In the manual, it states:
> "The order of the elements is: x1x1, x1y1, x1z1, x1x2, ..."
>
> Does "1" and "2" refer to the particles in the group?  I'm asking b/c my
> particular covar.dat file is of dimmensions 1934427 X 3 , for a group of
> about 100 atoms and a traj of 1 NS.  Just trying to make sense out of it
> . . .
>
> Thanks,
>
> Arneh
>
>
>
> Tsjerk Wassenaar wrote:
> > Hi Arneh,
> >
> > Yes. As you should be able to recall, the (linear, not "generalized")
> > correlation is formally given as:
> >
> > cor(x,y) = cov(x,y) / ( sqrt(var(x))*sqrt(var(y)) )
> >
> > The diagonal elements of the covariance matrix give the variances...
> >
> > Cheers,
> >
> > Tsjerk
> >
> > On 8/31/07, Arneh Babakhani <ababakha at mccammon.ucsd.edu> wrote:
> >
> >> Sorry for the confusion . I want the correlation.  So I can just use
> >> g_covar to get the covar. matrix, and divide each term by what you stated,
> >> to get the correlation matrix? (if I follow you correctly).
> >>
> >> Thanks,
> >>
> >>
> >>> Hi Arneh,
> >>>
> >>> You're not clear on what you want. Is it a covariance matrix or a
> >>> correlation matrix. Correlation and covariance are different things.
> >>> g_covar lets you write out a covariance matrix using the option
> >>> -ascii. In case you want the correlation matrix (though IIRC Karplus
> >>> also used the covariance matrix), you have to divide each element m_ij
> >>> by sqrt(m_ii)*sqrt(m_jj).
> >>>
> >>> Cheers,
> >>>
> >>> Tsjerk
> >>>
> >>> On 8/31/07, Arneh Babakhani <ababakha at mccammon.ucsd.edu> wrote:
> >>>
> >>>> Can anyone briefly recommend a procedure for calculating the correlation
> >>>> matrix (not the diagonalized covariance matrix, as done by g_covar) of a
> >>>> specified group?
> >>>>
> >>>> In particular, I'm looking to calculate the covariance matrix, as
> >>>> specifed
> >>>> in the Karplus paper (Proteins: Vol 11:205-217, 1991), where each entry
> >>>> of
> >>>> the matrix is defined as the correlation between the i-th and j-th atom:
> >>>>
> >>>> c_ij = <delta r_i> <delta r_j>
> >>>>
> >>>> where delta r is the deviation of i from its average position, averaged
> >>>> over the ensemble.
> >>>>
> >>>> Or, is there a way to use g_covar and suppress the diagonalization step,
> >>>> so as to obtain only the translation correlation matrix??? (I couldn't
> >>>> find anything to this effect in the manual).
> >>>>
> >>>> Much thanks,
> >>>>
> >>>> Arneh
> >>>>
> >>>> _______________________________________________
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> >>>>
> >>>>
> >>> --
> >>> Tsjerk A. Wassenaar, Ph.D.
> >>> Junior UD (post-doc)
> >>> Biomolecular NMR, Bijvoet Center
> >>> Utrecht University
> >>> Padualaan 8
> >>> 3584 CH Utrecht
> >>> The Netherlands
> >>> P: +31-30-2539931
> >>> F: +31-30-2537623
> >>>
> >>>
> >>
> >
> >
> >
>


-- 
Tsjerk A. Wassenaar, Ph.D.
Junior UD (post-doc)
Biomolecular NMR, Bijvoet Center
Utrecht University
Padualaan 8
3584 CH Utrecht
The Netherlands
P: +31-30-2539931
F: +31-30-2537623