gmx covar calculates and diagonalizes the (mass-weighted) covariance matrix. All structures are fitted to the structure in the structure file. When this is not a run input file periodicity will not be taken into account. When the fit and analysis groups are identical and the analysis is non mass-weighted, the fit will also be non mass-weighted.
The eigenvectors are written to a trajectory file (-v). When the same atoms are used for the fit and the covariance analysis, the reference structure for the fit is written first with t=-1. The average (or reference when -ref is used) structure is written with t=0, the eigenvectors are written as frames with the eigenvector number as timestamp.
Option -ascii writes the whole covariance matrix to an ASCII file. The order of the elements is: x1x1, x1y1, x1z1, x1x2, ...
Option -xpm writes the whole covariance matrix to an .xpm file.
Option -xpma writes the atomic covariance matrix to an .xpm file, i.e. for each atom pair the sum of the xx, yy and zz covariances is written.
Note that the diagonalization of a matrix requires memory and time that will increase at least as fast as than the square of the number of atoms involved. It is easy to run out of memory, in which case this tool will probably exit with a 'Segmentation fault'. You should consider carefully whether a reduced set of atoms will meet your needs for lower costs.