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6.12 largelyap - Compute separation of nearby trajectories

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)))
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