[gmx-users] Correlation Matrix Calculation

[Arneh Babakhani]

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
>>>
>>>       
>>     
>
>
>