Re: [AMBER] PCA variance using Freq = 108.587 * sqrt( 0.6 / Eigenvalue )

From: Muthukumaran R <kumaran.bicpu.edu.in>
Date: Mon, 26 Jan 2015 11:10:25 +0530

To calculate variance, it is necessary to obtain all the eigen values of a
system. This can be obtained using 'thermo' keyword and 'thermo' runs only
with mass-weighted covariance matrix.
Hence mass-weighted covariance matrix was used.

Is there any other way to calculate variance without using mass-weighted
covariance matrix ?

On Sun, Jan 25, 2015 at 9:53 PM, Daniel Roe <daniel.r.roe.gmail.com> wrote:

> Hi,
>
> The actual formula is:
>
> Freq. = TO_CM1 * sqrt( KT / Eigenvalue)
>
> where TO_CM1 is a constant for converting from original eigenvalue
> units to units of frequency (was 108.587 in ptraj but has much higher
> precision in cpptraj) and KT is Boltzmann's constant time temperature
> in Kelvin (originally in ptraj this was hardcoded to 0.6 kcal/mol, but
> in recent versions of cpptraj you can specify the temperature during
> 'diagmatrix'). So according to this, the conversion the other way is:
>
> Eigenvalue = KT / (Freq. / TO_CM1)^2
>
> If I plug your first frequency (0.48444 cm^-1) into this (using
> 108.587 and 0.6 for TO_CM1 and KT respectively) I get ~30145 Ang.^2 *
> amu.
>
> However, is there a reason you chose to mass-weight your covariance
> matrix in the first place? If all you want to do is PCA you should
> just use the coordinate covariance matrix (i.e. 'matrix covar'). I
> think the only real reason you'd want to mass-weight your covariance
> matrix is if you want to perform quasi-harmonic analysis.
>
> Hope this helps,
>
> -Dan
>
> On Sun, Jan 25, 2015 at 8:42 AM, Muthukumaran R <kumaran.bicpu.edu.in>
> wrote:
> > Dear Amber users,
> >
> > I am performing PCA calculations using cpptraj in ambertools 14.
> > There are 630 C-alpha atoms in my protein and the mass-weighted
> covariance
> > matrix is 1890 x 1890.
> >
> > I extracted the eigenvalues and the first 5 are given below.
> >
> > 1 0.48444
> > 2 0.58309
> > 3 1.08605
> > 4 1.58621
> > 5 1.98272
> >
> > I want to calculate the percentage of variance for each eigenvector.
> >
> > According to the suggestions given in the mailing list, I understand that
> > these are frequencies and should be converted to eigenvalues for
> > calculating variance.
> >
> > I tried to convert them using the conversion formula,
> > Freq = 108.587 * sqrt( 0.6 / Eigenvalue )
> >
> > (http://archive.ambermd.org/201307/0678.html)
> >
> > But, the first frequency gave a very small eigenvalue (in the range of
> e-06)
> >
> > Am I proceeding in the right direction?
> >
> > I need your valuable suggestions in calculating the percentage variance
> of
> > each eigenvector.
> >
> >
> > _______________________________________________
> > AMBER mailing list
> > AMBER.ambermd.org
> > http://lists.ambermd.org/mailman/listinfo/amber
>
>
>
> --
> -------------------------
> Daniel R. Roe, PhD
> Department of Medicinal Chemistry
> University of Utah
> 30 South 2000 East, Room 307
> Salt Lake City, UT 84112-5820
> http://home.chpc.utah.edu/~cheatham/
> (801) 587-9652
> (801) 585-6208 (Fax)
>
> _______________________________________________
> AMBER mailing list
> AMBER.ambermd.org
> http://lists.ambermd.org/mailman/listinfo/amber
>
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Received on Sun Jan 25 2015 - 22:00:02 PST
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