How to calculate the covariance matrix and the cross-correlation matrix

Dear all,

I have two sets of 3D coordinate {x y z}data (please see the two attached files: P1-coordinate.txt and P3-coordinate.txt). Each of the two files contains the information for the positions (coordinates) of 9 atoms at 5 time points in the 3D space.The coordinates of the 9 atoms at two adjacent time points are seperated by a blank line. And the 5 time ponts (t1, t2, t3, t4, t5) are the same for the two files. Now I want to calculate the covariance matrix (cij) and the cross-correlation matrix (Cij) of these two sets of atoms.

The cij is defined as the following:

where ri and rj are the position vectorof atom i and j at time t, which are listed in the P1-coordinate.txt and P1-coordinate.txt, repectively; Angle brackets denote time averages; taver is the averaging time and Dt the time interval between two time points.

The cross-correlation matrix (Cij) is defined as the following:

Can these calculation be realized in Matlab?

Best regards.

Yeping Sun

[Naomi Krauzig]

If this is still an open question there is a 3d version available https://it.mathworks.com/matlabcentral/fileexchange/65640-spatialcorr3-varargin.

Hope it helps.

All the best,

Naomi