[gmx-users] g_sham -dim ? (fwd)

[Berk Hess]

>From: David van der Spoel <spoel at xray.bmc.uu.se>
>Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>Subject: Re: [gmx-users] g_sham -dim ? (fwd)
>Date: Mon, 12 Mar 2007 14:26:23 +0100
>
>
>>>---------- Forwarded message ----------
>>>Date: Mon, 12 Mar 2007 11:40:54 +0100 (CET)
>>>From: Alexandra Patriksson <alexandra at xray.bmc.uu.se>
>>>To: gmx_users at gromacs.org
>>>Subject: g_sham -dim ?
>>>
>>>
>>>I would like to do a 3D-histogramanalysis using three principal 
>>>components derived from a PCA analysis using all coordinates of a protein 
>>>trajectory, but is a bit confused about the -dim flag. If I use -dim 3 3 
>>>3 (because of distances in three dimensions) I either get Ptot = Inf or 
>>>Fatal error, depending on which version of the program I use. My question 
>>>is - should I use this -dim flag at all or can I keep it at the default 
>>>value of 1 1 1 ?
>>
>>Each principal component is a single dimension, not a distance
>>between two particles in 3D space.
>>Therefore you should use 1 1 1.
>>
>>Berk.
>>
>But isn't a principal component a distance from a point (the average)?

You could see a principal component as the distance from the average
along a certain direction. But this is not a distance between particles
in an n-dimensional space.

To be more precise: in principal component analysis one does a linear
transformation of the coordinates.
Problems arise in histogram methods when a non-linear transformation
is applied. As in the case where you want to go from a difference
vector between two particles in Cartesian coordinates to a vector
length and two angles. If one then bins lengths, one has to take
the Jacobian of this transformation into account. That is what the -dim
option of g_sham does.

Berk.

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