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From: Daniel Roe <daniel.r.roe.gmail.com>

Date: Wed, 28 Jan 2015 08:26:03 -0700

Hi,

On Sun, Jan 25, 2015 at 10:40 PM, Muthukumaran R <kumaran.bicpu.edu.in> wrote:

*> 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 ?
*

I'm not clear on what you mean by 'variance' here. It's not necessary

to mass-weight a coordinate covariance matrix to obtain eigenvalues,

but it does change the units (when mass-weighted eigenvalues are

converted to frequencies to enable quasi-harmonic analysis). In your

original email you mention PCA, which implies (to me at least) using

the non-mass-weighted coordinate covariance matrix. Maybe if you

provide some more details on the analysis you're trying to perform I

can try to give more specific advice.

-Dan

*>
*

*>
*

*>
*

*>
*

*> 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.
*

*>> >
*

*>> >
*

*>> > Thanks in advance..
*

*>> > _______________________________________________
*

*>> > 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
*

*>>
*

*> _______________________________________________
*

*> AMBER mailing list
*

*> AMBER.ambermd.org
*

*> http://lists.ambermd.org/mailman/listinfo/amber
*

Date: Wed, 28 Jan 2015 08:26:03 -0700

Hi,

On Sun, Jan 25, 2015 at 10:40 PM, Muthukumaran R <kumaran.bicpu.edu.in> wrote:

I'm not clear on what you mean by 'variance' here. It's not necessary

to mass-weight a coordinate covariance matrix to obtain eigenvalues,

but it does change the units (when mass-weighted eigenvalues are

converted to frequencies to enable quasi-harmonic analysis). In your

original email you mention PCA, which implies (to me at least) using

the non-mass-weighted coordinate covariance matrix. Maybe if you

provide some more details on the analysis you're trying to perform I

can try to give more specific advice.

-Dan

-- ------------------------- 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/amberReceived on Wed Jan 28 2015 - 07:30:04 PST

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