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# 6.7 `corrsum` - Computation of the correlation sum

The topics correlation sum and correlation dimension estimation can also be found here.

Syntax:

- `[c, d] = corrsum(pointset, query_indices, range, exclude)`
- `[c, d] = corrsum(pointset, query_indices, range, exclude, bins)`
- `[c, d] = corrsum(atria, pointset, query_indices, range, exclude)`
- `[c, d] = corrsum(atria, pointset, query_indices, range, exclude, bins)`

Input arguments:

- `atria` - output of nn_prepare for pointset (optional) (cf. Section 6.13)
- `pointset` - a `N` by `D` double matrix containing the coordinates of the point set, organized as `N` points of dimension `D`
- `query_indices` - query points are taken out of the pointset, query_indices is a vector of length `R` which contains the indices of the query points (indices may vary from 1 to N)
- `range` - search range, may be given in one of two ways
  - If only a single value is given, this value is taken as maximal search radius relative to the attractor diameter (0 relative_range 1). The minimal search radius is determined automatically be searching for the minimal interpoint distance in the data set.
  - If a vector of length two is given, the values are interpreted as absolut minimal and maximal search radius.
- `exclude` - in case the query points are taken out of the pointset, exclude specifies a range of indices which are omitted from search. For example if the index of the query point is 124 and exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0 means: exclude self-matches
- `bins` - number of distance values at which the correlation sum is evaluated, defaults to 32

Output arguments:

- `c` - vector of correlation sums, `length(c) = bins`
- `d` - vector of the corresponding distances at which the correlation sums (stored in `c`) were computed. `d` is exponentially spaced, `length(c) = bins`

Example:

    x = chaosys(25000, 0.025, [0.1 -0.1 0.02], 0);  % generate data from Lorenz system
    x = x(5001:end,:);      % discard first 5000 samples due to transient
    % now compute correlation sum up to five percent of attractor diameter
    [c,d] = corrsum(x, randref(1,20000, 1000), 0.05, 0);
    loglog(d,c)     % and show the result as log-log plot

Next: 6.8 corrsum2 - Computation Up: 6. Mex-Function Reference Previous: 6.6 chaosys - integrate Contents