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largelyap is an algorithm very similar to the Wolf algorithm [90]
, it computes the average exponential
growth of the distance of neighboring orbits via the prediction error. The increase of the prediction error
vs the prediction time allows an estimation of the largest lyapunov exponent.
Syntax:
- x = largelyap(pointset, query_indices, taumax, k
exclude)
- x = largelyap(atria, pointset, query_indices, taumax, k
exclude)
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)
- taumax - maximal time shift
- k - number of nearest neighbors to compute
- 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
Output arguments:
- x - vector of length taumax+1, x(tau) = 1/Nref * sum(log2(dist(reference point + tau, nearest neighbor + tau)/dist(reference point,
nearest neighbor)))
[146]
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