[gmx-users] Correlation Matrix Calculation

[Tsjerk Wassenaar]

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