# TOOLBOX

WE ARE REWORKING THE PROGRAMMES, A NEW VERSION WILL BE AVAILABLE SOON

have a look to the functions wich will be included in this toolbox: reference manual

the toolbox contains MATLAB routines for computing recurrence plots and related problems as M-files

parameters in [ ] are optional

sorry, software is only available for members of the nonlinear dynamics group

also visit mathtools.net to survey other useful toolboxes
still under construction,

routine description
recurrence plot, cross recurrence plot CRP(X [,Y [,M,T,E,A]])

creates a cross recurrence plot/ recurrence plot results could be stored into the workspace

allows to change the parameters interactively by using a GUI

the source-data X and test-data Y can be one- or a two-coloumn vectors (then, in the first column have to be the time); if the test-data Y is not specified, a simple recurrence plot is created

parameters: dimension M, delay T and the size of neighbourhood E; the flag A allows to switch between various methods of finding neighbours or CRPs, resp.:
A=1 -> Euclidean norm
A=2 -> Euclidean norm between normalized vectors
A=3 -> fixed amount of neighbours
A=4 -> distance coded matrix (global CRP)
parameters not needed to specify

current limitation: for higher speed in output the whole matrix of the recurrence plot is in the work space - this limits the application of long data series

complexity measures based on (cross) recurrence plots CRQA(X [,Y [,W,M,T,E,L,A]])

recurrence quantification analysis (WEBBER) vs. time (away from mean diagonal) of cross-recurrence with the first vector X and the second Y Lmin is the minimal length for a line if W=[] then the whole plot will calculated B is the maximum forwarded (backwarded) time J=time scale
Y(1)=RR of diagonalline
Y(2)=DET
Y(3)=L
Y(4)=ENTR

length of vertical lines in recurrence plots TT mean trapping time and its distribution.

A=TT(X) computes the mean of the length of the vertical line structures in a recurrence plot, so called trapping time TT.

[A B]=TT(X) computes the TT and the distribution of the length of the vertical line structures, stored in B.

estimation main diagonal path of a RP [X, Y]=TRACK(RP)

estimates the path of the main diagonal line in a RP
RP is a N x N-Matrix

heaviside function Y=H(X)

heaviside function y=H(x) with
y=1 for x>=0 and
y=0 for x<0

X can be an one-column or one-row vector

transformation to pretended distibutions Y=TRAFO(X [,A])

transformation of data X to a pretended distribution Y, where
A=0 normal distribution (defeault),
A=1 uniform distribution,
A=2 exponential distribution

X is an one-column or two-column vector (then, in the first column have to be the time)

mutual information S=MI(X1, X2, T, [,A])

mutual information between the data in the vectors X1 and X2
(A=0 -> without plot)

X1 and X2 are one-column vectors

auto mutual information M=autoMI(X, T)

computes the auto mutual information of the vector X

X is an one-column or two-column vector (then, in the first column have to be the time) vectors

estimation entropy E=ENTROPY(X)

estimates the entropy E of a vector X

phase space diameter [Y Z]=PSS(X,M,T)

computes the maximal (Y) and the averaged (Z) phase space diameter of data X, with the embedding parameters dimension M and lag T

walsh transformation Y=WALSH(X)

computes the walsh transformation s=walsh(x) where
Y and X are one-column vectors

walsh power spectrum Y=WALSHPOWER(X)

computes the walsh power spectrum s2=(walsh(x))2 where
Y and X are one-column vectors

etc.