CRP Toolbox Reference |

## crqa## PurposeComputes and plots the CRQA measures.## Syntaxcrqa(x)crqa(x,y) y=crqa(x,y,m,t,e,w,ws) y=crqa(x,y,m,t,e,w,ws,lmin,vmin) y=crqa(x,y,m,t,e,w,ws,lmin,vmin,tw) y=crqa(x,y,m,t,e,[],'param1','param2',...) ## DescriptionRecurrence quantification analysis of cross-recurrence
with the first vector 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. ## ParametersDimension
As the last numeric parameter, the size of the Theiler window 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).
Parameters not needed to be specified.
The window of length ## NoteA prototype for estimation of confidence intervals for RQA measures is available at http://www.agnld.uni-potsdam.de/~schinkel/rqaci.php. We plan to include it in the CRP toolbox in the near future. ## LimitationsFor 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 ## WarningThe RQA measures may differ from those of the RQA programmes by Charles Webber Jr. For compatibility use a Theiler window of size one and ensure that the data are normalized before by the same distance which is used in the RQA programmes; e.g. normalize with the maximal phase space diameter, which can be estimated with the programme pss:
RQA=crqa(100*x/pss(x,dim,lag,'euclidean'),dim,lag,e,[],[],l_min,v_min,1,...
'euclidean','nonormalize','silent') ## Examplesa=randn(300,1);crqa(a,1,1,.2,40,2,'euc')
N=300; w=40; ws=2;a=3.4:.6/(N-1):4; b=.5; for i=2:N, b(i)=a(i)*b(i-1)*(1-b(i-1));end y=crqa(b,3,2,.1,w,ws); subplot(2,1,1), plot(a,b,'.','markersize',.1) title('logistic map'), axis([3.4 4 0 1]) subplot(2,1,2), plot(a(1:ws:N-w),y(1:ws:N-w,1)) ylabel('recurrence rate'), axis([3.4 4 0 1]) ## See Also## ReferencesMarwan, N., Romano, M. C., Thiel, M., Kurths, J.: Recurrence Plots for the Analysis of Complex Systems, Phys. Rep., 438, 2007. Little, M., McSharry, P., Roberts, S., Costello, D., Moroz, I.: Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection, Biomed. Eng. Online, 6, 2007. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: Structures and dynamics, Phys. Rep., 424, 2006. Marwan, N., Donges, J. F., Zou, Y., Donner, R. V., Kurths, J.: Complex network approach for recurrence analysis of time series, Phys. Lett. A, 373(46), 2009. |

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