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C++ API

Function File: [lyap_exp, pars] = lyap_spec (S)
Function File: [lyap_exp, pars] = lyap_spec (S, paramName, paramValue, …)

Estimates the spectrum of Lyapunov exponents using the method of Sano and Sawada.

Input

S

This function always assumes that each time series is along the longer dimension of matrix S. It also assumes that every dimension (counting along the shorter dimension) of S is considered a component of the time series.

Parameters

m

Embedding dimension [default = 2].

d

Currently unused, will be delay used in future.

n

Number of iterations [default = length (S)].

r

Minimum neighborhood size [default = 1e-3].

f

Factor to increase the size of the neighborhood if the program didn’t find enough neighbors [default = 1.2].

k

Number of neighbors to use (this implementation uses exactly the number of neighbors specified, if more are found only the K nearest are used) [default = 30].

p

Specify after how many iteration should the current output be displayed. This is useful for data sets that can take a long time. Also, if the program runs longer than 10 seconds it will display the current state, regardless [default = calculate all of the data at once and don’t intermediary steps].

Switch

invert

Inverts the order of the time series. Can help finding spurious exponents.

Output

The output is alligned with the components of the input.

lyap_exp

Assuming an input with column vectors this part of the output will consist of columns (S) * m + 1 columns (the ’m’ stands for the embedding dimension). The first column will be the iteration number and rest contain estimates of the Lyapunov exponents in decreasing order.

pars

This is a struct that contains the following parameters associated with the calculated Lyapunov exponents:

  • rel_err - the relative error for every dimension of the input
  • abs_err - the absolute error for every dimension of the input
  • nsize - average neighborhood size
  • nno - average number of neighbors
  • ky_dim - estimated KY-Dimension

See also: lyap_k, lyap_r.

Algorithms

The algorithms for this functions have been taken from the TISEAN package.

Package: tisean