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

L. Michel Espinoza-Fonseca mef at ddt.biochem.umn.edu
Sat Feb 16 04:17:42 CET 2008

```Hi Tsjerk,

Indeed it does make sense! Thanks for you comments.

Cheers,
Michel

PS. After all it wasn't a waste of time, isn't it? :)

On Feb 15, 2008 4:53 AM, Tsjerk Wassenaar <tsjerkw at gmail.com> wrote:
> 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
> >  >  >  >  phone: ++49-551-2012312
> >  >  >  >  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
> 3584 CH Utrecht
> The Netherlands
> P: +31-30-2539931
> F: +31-30-2537623
> _______________________________________________
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