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

From: Daniel Roe <daniel.r.roe.gmail.com>
Date: Sun, 25 Jan 2015 09:23:35 -0700

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
'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.
>
>
> _______________________________________________
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> AMBER.ambermd.org
> http://lists.ambermd.org/mailman/listinfo/amber

```--
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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)
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Received on Sun Jan 25 2015 - 08:30:05 PST
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