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.

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 |

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.

See also d2

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