Description of the program: xc2

Cross-correlation integral of two N-dimensional data sets given in two files. Together with the (auto-)correlation integrals of each of the two sets, this gives an impression of their similarity or dissimilarity. If the minimal number of centers n is small, the program is fast but the results suffer from large statistical fluctuations on the large length scales. Apart from statistical fluctuations, the results are invariant under the exchange of the sequence of the two files.

Usage:

xc2 [options] file1 file2

Everything not being a valid option will be interpreted as a potential datafile name.

Possible options are:

Option Description Default

-M#,# dimension of the data sets (the same for both!),
maximal embedding dimension 1,2

-n# minimal number of centers 1000

-d# delay for the embedding (the same for both data sets) 1

-N# maximal number of pairs for each length scale 1000

-## number of length scale values 2 per octave

-r# minimal length scale smallest distance of points in 2 dimensions

-R# maximal length scale MAX(xmax-xmin,ymax-ymin)

-l# maximal number of values to read (file1) read whole file

-x# number of lines to be skipped (file1) 0

-L# maximal number of values to read (file2) read whole file

-X# number of lines to be skipped (file2) 0

-c#[,#] columns to be read 1,2,...

-o# output file name file1_file2_xc2

-V# verbosity level (0 = report only fatal errors) 1

-h show these options none

Option	Description	Default
-M#,#	dimension of the data sets (the same for both!), maximal embedding dimension	1,2
-n#	minimal number of centers	1000
-d#	delay for the embedding (the same for both data sets)	1
-N#	maximal number of pairs for each length scale	1000
-##	number of length scale values	2 per octave
-r#	minimal length scale	smallest distance of points in 2 dimensions
-R#	maximal length scale	MAX(xmax-xmin,ymax-ymin)
-l#	maximal number of values to read (file1)	read whole file
-x#	number of lines to be skipped (file1)	0
-L#	maximal number of values to read (file2)	read whole file
-X#	number of lines to be skipped (file2)	0
-c#[,#]	columns to be read	1,2,...
-o#	output file name	file1_file2_xc2
-V#	verbosity level (0 = report only fatal errors)	1
-h	show these options	none

Description of the Output:

Output: file file1_file2_xc2,
It consists of separate blocks for each embedding space starting with either m=2, ranging to m=M for univariate data, or starting at N and ending at NxM for multivariate data (adding the extra dimensions one by one). Inside each block the second column gives the fraction of pairs of points with distance smaller than the value reported in the first column. It has to be looked at on a log-log plot. For a discussion of its usefulness consult the original research article by H. Kantz, Quantifying the closeness of fractal measures, Phys. Rev. E 49, 5091-5097 (1994).

View the FORTRAN source.