g_anaeig Main Table of Contents

VERSION 3.1 Thu 28 Feb 2002

Description

g_anaeig analyzes eigenvectors. The eigenvectors can be of a covariance matrix (g_covar) or of a Normal Modes anaysis (g_nmeig).

When a trajectory is projected on eigenvectors, all structures are fitted to the structure in the eigenvector file, if present, otherwise to the structure in the structure file. When no run input file is supplied, periodicity will not be taken into account. Most analyses are performed on eigenvectors -first to -last, but when -first is set to -1 you will be prompted for a selection.

-disp: plot all atom displacements of eigenvectors -first to -last.

-proj: calculate projections of a trajectory on eigenvectors -first to -last. The projections of a trajectory on the eigenvectors of its covariance matrix are called principal components (pc's). It is often useful to check the cosine content the pc's, since the pc's of random diffusion are cosines with the number of periods equal to half the pc index. The cosine content of the pc's can be calculated with the program g_analyze.

-2d: calculate a 2d projection of a trajectory on eigenvectors -first and -last.

-3d: calculate a 3d projection of a trajectory on the first three selected eigenvectors.

-filt: filter the trajectory to show only the motion along eigenvectors -first to -last.

-extr: calculate the two extreme projections along a trajectory on the average structure and interpolate -nframes frames between them, or set your own extremes with -max. The eigenvector -first will be written unless -first and -last have been set explicitly, in which case all eigenvectors will be written to separate files. Chain identifiers will be added when writing a .pdb file with two or three structures (you can use rasmol -nmrpdb to view such a pdb file).

Overlap calculations between covariance analysis:
NOTE: the analysis should use the same fitting structure

-over: calculate the subspace overlap of the eigenvectors in file -v2 with eigenvectors -first to -last in file -v.

-inpr: calculate a matrix of inner-products between eigenvectors in files -v and -v2. All eigenvectors of both files will be used unless -first and -last have been set explicitly.

When -v, -eig1, -v2 and -eig2 are given, a single number for the overlap between the covariance matrices is generated. The formulas are:
difference = sqrt(tr((sqrt(M1) - sqrt(M2))^2))
normalized overlap = 1 - difference/sqrt(tr(M1) + tr(M2))
shape overlap = 1 - sqrt(tr((sqrt(M1/tr(M1)) - sqrt(M2/tr(M2)))^2))
where M1 and M2 are the two covariance matrices and tr is the trace of a matrix. The numbers are proportional to the overlap of the square root of the fluctuations. The normalized overlap is the most useful number, it is 1 for identical matrices and 0 when the sampled subspaces are orthogonal.

Files

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