[gmx-users] Normal Mode Analysis on Calphas only ??

[Berk Hess]

Here is the formula (thanks to Herman Berendsen).
I was slightly wrong. You first need to reduce the Hessian
and then diagonalize the C-alpha only Hessian.

definitions:
Interesting particle coordinates: x
Uninsteresting particle coordinates y
full hessian in terms of (x, y): H

Split H into four blocks:

     Hxx    Hxy
H =
     Hyx    Hyy

Then the hessian H' in the subspace of x coordinates, under the condition 
that the y coordinates are in a minimum, is

H' = Hxx - Hxy Hyy^-1 Hyx

This is a simple transformation, requiring only one inversion and two matrix 
multiplications.

Berk.

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