CRP Toolbox Reference

crqad

Purpose

Computes and plots the diagonalwise CRQA measures.

Syntax

    crqad(x)
    crqad(x,y)
    y=crqad(x,y,m,t,e,w)
    y=crqad(x,y,m,t,e,w,lmin)
    y=crqad(x,y,m,t,e,[],'param1','param2',...)

Description

Recurrence quantification analysis of diagonals in the cross recurrence plot of the vectors x and y as well as x and -y for the diagonals within the range [-w,w] around the main diagonal. The output is a structure (see below).

The input vectors can be multi-column vectors, where each column will be used as a component of the phase-space vector. However, if the first column is monotonically increasing, it will be used as an time scale for plotting.

Parameters

Dimension m, delay t, the size of neighbourhood e and the range size w are the first five numbers after the data series; if w=[] then the whole plot will be calculated. Variable lmin sets the minimal length of what should be considered to be a diagonal line. Further parameters can be used to switch between various methods of finding the neighbours of the phasespace trajectory, to suppress the normalization of the data and to suppress the GUI (useful in order to use this programme by other programmes).

Methods of finding the neighbours.
   'maxnorm' Maximum norm.
   'euclidean' - Euclidean norm.
   'minnorm' Minimum norm.
   'nrmnorm' - Euclidean norm between normalized vectors
(all vectors have the length one).
   'rr' Maximum norm, fixed recurrence rate.
   'fan' - Fixed amount of nearest neighbours.
   'inter' - Interdependent neighbours.
   'omatrix' - Order matrix.
   'opattern' - Order patterns recurrence plot.

Normalization of the data series.
   'normalize' - Normalization of the data.
   'nonormalize' - No normalization of the data.

Suppressing the GUI.
   'gui' - Creates the GUI and the output plot.
   'nogui' - Suppresses the GUI and the output plot.
   'silent' - Suppresses all output.

Output
   y.RRp - Recurrence rate for (x,y).
   y.RRm - Recurrence ratefor (x,y).
   y.DETp - Determinism (x,y).
   y.DETm - Determinism (x,-y).
   y.Lp - Averaged diagonal length (x,y).
   y.Lm - Averaged diagonal length (x,-y).

Parameters not needed to specify.

Limitations

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. However, a solution for using long data series you can find under the description for crp, or by using the command crqad_big.

Examples

    a=sin(0:.1:80)+randn(1,801);
    b=sin(0:.1:80)+randn(1,801);
    crqad(a,b,3,15,.1,100,'fan')

Remarks

A GUI for this task is under development.

See Also

crqad, crqa, crp, dl, tt, rpde

References

Marwan, N., Kurths, J.: Nonlinear analysis of bivariate data with cross recurrence plots, Phys. Lett. A, 302, 2002.

crqa crqad_big