# Description of the program: lyap_spec

This program estimates the whole spectrum of Lyapunov exponents for a given scalar time series. Whole spectrum means: If the embedding dimension is d than 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# | embedding dimension (and number of exponents to estimate) | 2
-d# | delay for the delay vectors | 1
-r# | initial size of the neighborhoods is dynamically changed during the run | (data interval)/1000
-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 m+1 columns. The first one shows the actual iteration, the next m ones the estimates of the Lyapunov exponents in decreasing order. The last three lines show the average forecast error 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.

View the C-sources.

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