# [gmx-users] eigenvalues as a function of time

Tsjerk Wassenaar tsjerkw at gmail.com
Fri Feb 15 11:53:40 CET 2008

Hi Michel,

Mind the eigenvectors! If you want to know how the eigenvalues
converge, you also have to take the convergence of your eigenvectors
into account. It may well be that for one subtrajectory one
eigenvector is dominant, but that for a longer subtrajectory another
is getting more important. Now, in fact any decomposition is as good
as any other, so your best estimate for the eigenvectors to look along
is the set obtained from the total covariance analysis. You then
probably want to look at the convergence of the eigenvalues along
these modes, which are basically the variances of the projections on
these modes. In that case, you're best bet is likely to calculate the
variances of the projections for each subtrajectory with respect to
the corresponding average projections. The average projections all
converge to 0, by definition and the variances will thus converge to
the eigenvalues.

O yes, this saves you quite a bit of time constructing and
diagonalizing covariance matrices.

I hope this makes sense to you :)

Best,

Tsjerk

On Fri, Feb 15, 2008 at 7:23 AM, L. Michel Espinoza-Fonseca
<mef at ddt.biochem.umn.edu> wrote:
> Hi Tsjerk,
>
>  You are right. I think that by either lack of caffeine or attention
>  (most probably the second one) I wrote the intervals in a wrong way. I
>  just realized it now thanks to your email. So, going back to my
>  original post, I want to obtain the eigenvalues vs time, so then I can
>  use them to calculate the entropy of a X system using the
>  quasi-harmonic approximation. What I realized (if I'm correct this
>  time) is that I need to calculate the covariance matrix *not* from
>  isolated intervals (such as 0-500, 501-1000, etc.) but from intervals
>  starting from the reference structure (0-500, 0-1000, 0-1500, etc.).
>  The goal is simply to determine to what extend the entropy converges
>  in the simulation, as it has been shown that relatively long
>  simulations are needed for this term to converge.
>
>  On the other hand, splitting wasn't the right word, after all. Even
>  now I can't find the right word. I slipped up twice.
>
>  I apologize for my mistake -I basically took from you a few minutes
>  because of my lack of clarity :)
>
>  Cheers,
>  Michel
>
>
>
>  On Thu, Feb 14, 2008 at 11:47 PM, Tsjerk Wassenaar <tsjerkw at gmail.com> wrote:
>  > Hi Michel,
>  >
>  >  You're principal components will be heavily undersampled (and
>  >  therefore underdetermined), most notably the higher ones. You're
>  >  likely not even to have more than a single uncorrelated observation
>  >  per subtrajectory. The eigenvalue is a measure of the fluctuation, or
>  >  actually the spread, over time. It's not that trivial to split that.
>  >  Also note that we usually neglect the fact that we have too few
>  >  independent observations in a trajectory as it is. You're just making
>  >  things worse.
>  >
>  >  Cheers,
>  >
>  >  Tsjerk
>  >
>  >
>  >
>  >  On Thu, Feb 14, 2008 at 11:33 PM, L. Michel Espinoza-Fonseca
>  >  <mef at ddt.biochem.umn.edu> wrote:
>  >  > Mark,
>  >  >
>  >  >  I have one more question. For example, if I have a trajectory of 10 ns
>  >  >  divided in intervals of 10 ps each, to obtain a set of eigenvalues
>  >  >  each 500 ps I have to calculate the eigenvalues using the following
>  >  >  intervals:
>  >  >
>  >  >  0-500 ps
>  >  >  501-1000 ps
>  >  >  1001-1500 ps
>  >  >  ....
>  >  >  9501-10000 ps
>  >  >
>  >  >  Is that correct?
>  >  >
>  >  >  Thanks!
>  >  >
>  >  > Michel
>  >  >
>  >  >  On Thu, Feb 14, 2008 at 2:54 AM, Marcus Kubitzki <mkubitz at gwdg.de> wrote:
>  >  >
>  >  >
>  >  > > Hi Michel,
>  >  >  >
>  >  >  >  I'm confused by what you mean by "splitting" the eigenvalues.
>  >  >  >  With g_covar -b -e you can get eigenvals for a specified interval of
>  >  >  >  time, e.g. 0-1ns. Getting eigenvals as a function of time (if that's
>  >  >  >  what I suspect you want to do), you need to run g_covar for all
>  >  >  >  intervals 0-t1, 0-t2, 0-t3, ... to get the desired sequence.
>  >  >  >
>  >  >  >  Marcus
>  >  >  >
>  >  >  >
>  >  >  >
>  >  >  >
>  >  >  >  L. Michel Espinoza-Fonseca wrote:
>  >  >  >  > Hi all,
>  >  >  >  >
>  >  >  >  > I have a MD trajectory and want to split the eigenvalues as a function
>  >  >  >  > of time. I've been trying to do so with g_covar but with no success.
>  >  >  >  > I'd like to know if you could guide me on this matter. I'm planning to
>  >  >  >  > further used those values to calculate the entropy (By using Karplus'
>  >  >  >  > approximation) vs time and its convergence in the simulation.
>  >  >  >  >
>  >  >  >  > Cheers,
>  >  >  >  > Michel
>  >  >  >  > _______________________________________________
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>  >  >  >  --
>  >  >  >  Marcus Kubitzki
>  >  >  >  Max Planck Institute for Biophysical Chemistry
>  >  >  >  Computational Biomolecular Dynamics Group
>  >  >  >  Am Fassberg 11
>  >  >  >  D-37077 Göttingen
>  >  >  >  Germany
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>  >  >  >  fax: ++49-551-2012302
>  >  >  >  Email: mkubitz[at]gwdg.de
>  >  >  >  www: http://www.mpibpc.mpg.de/groups/de_groot/
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>  >
>  >
>  >  --
>  >  Tsjerk A. Wassenaar, Ph.D.
>  >  Junior UD (post-doc)
>  >  Biomolecular NMR, Bijvoet Center
>  >  Utrecht University
>  >  3584 CH Utrecht
>  >  The Netherlands
>  >  P: +31-30-2539931
>  >  F: +31-30-2537623
>  >
>  >
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--
Tsjerk A. Wassenaar, Ph.D.
Junior UD (post-doc)
Biomolecular NMR, Bijvoet Center
Utrecht University