Description of the program: lyap_spec

This program estimates the whole spectrum of Lyapunov exponents for a given, possibly multivariate, time series. Whole spectrum means: If d components are given and the embedding dimension is m than m*d exponents will be determined. The method is based on the work of Sano and Sawada.

Usage:

lyap_spec [Options]

Everything not being a valid option will be interpreted as a potential datafile name. Given no datafile at all, means read stdin. Also - means stdin

Possible options are:

Option Description Default
-l# number of points to use whole file
-x# number of lines to be ignored 0
-c# column to be read 1
-m#,# no. of components, embedding dimension 1,2
-r# minimal neighborhood size not set
-f# factor to increase the size of the neighborhood
if not enough neighbors were found 		1.2
-k# number of neighbors to use (this version uses exactly the number
of neighbors specified. If found more, only the # nearest will be used) 		30
-n# number of iterations number of points
-I invert the order of the time series.
Is supposed to help finding spurious exponents. 		no inversion
-o# output file name 'datafile'.lyaps
(or stdin.lyaps if data were read from stdin)
if no -o is given stdout is used
-V# verbosity level
  0: only panic messages
  1: add input/output messages 		1
-h show these options none

Description of the Output:

The output consists of d*m+1 columns. The first one shows the actual iteration, the next d*m ones the estimates of the Lyapunov exponents in decreasing order. The last lines show the average forecast error(s) of the local linear model, the average neighborhood size used for fitting the model and the last one the estimated Kaplan-Yorke dimension.
Output is written every 10 seconds (real time), approximately.

Remark on the delay embedding

In older versions of this program it was possible to change the delay of the embedding. This option was removed for the reason that the way the program handled this delay was not very efficient. Instead of rewriting everything, we decided to completely remove this option. In case you want to use delays other than 1, use the program delay to create a multivariate time series with the desired delay and read this multivariate time series into lyap_spec.
View the C-sources.
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