I'm having a hard time trying to found on the literature how to classify structures of the RPs, somebody could point me a reference or explain.
I am building my own code. The code can measure the length of the maximal main/secondary diagonal length and the maximal vertical/horizontal length of a structure of a RP. I supose, that I should say that a cluster is a main diagonal line, case the length of the main diagonal is much bigger then the other lengths, but I'm not sure it is the right way.
Identifying structures on RPs
 Norbert
 Expert
 Posts: 195
 Joined: Wed Jan 4, 2006 11:03
 Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
 Location: Potsdam, Germany
 Location: Potsdam Institute for Climate Impact Research, Germany
Re: Identifying structures on RPs
hello angelo,
i would say that the definitions of diagonal and vertical lines in a RP are quite clear and well explained in several publications, e.g., in
N. Marwan, M. C. Romano, M. Thiel, J. Kurths: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(56), 237329, DOI:10.1016/j.physrep.2006.11.001
simply speaking a diagonal line are connected points in a RP in diagonal direction, i.e., R_(i,i+j) = 1 for i=a,...,b.
your other question about the clusters is not really clear to me. are you asking to just remove the main diagonal?
best regards
norbert
PS: here is some example code how to fill a histogram of lengths of diagonal lines. here the histogram counts each diagonal line as two lines as finally i consider the entire RP (lower and upper triangle of the matrix) but the implementation considers only the lower triangle (and assumes that the RP is symmetric).
i would say that the definitions of diagonal and vertical lines in a RP are quite clear and well explained in several publications, e.g., in
N. Marwan, M. C. Romano, M. Thiel, J. Kurths: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(56), 237329, DOI:10.1016/j.physrep.2006.11.001
simply speaking a diagonal line are connected points in a RP in diagonal direction, i.e., R_(i,i+j) = 1 for i=a,...,b.
your other question about the clusters is not really clear to me. are you asking to just remove the main diagonal?
best regards
norbert
PS: here is some example code how to fill a histogram of lengths of diagonal lines. here the histogram counts each diagonal line as two lines as finally i consider the entire RP (lower and upper triangle of the matrix) but the implementation considers only the lower triangle (and assumes that the RP is symmetric).
Code: Select all
for ( i = 0; i < size; i++ ) { /* for each point */
counterL = 0;
for ( j = 0; j < sizei; j++ ) { /* look in diagonal direction */
/* compute the distance between the phase space points */
d = distance( dataPtr + cols * (i+j), dataPtr + cols * j );
/* check whether we have recurrence point */
if ( d < e && j < sizei) {
/* consider only RP outside the Theiler window */
if(i >= theilerCorr) ++counterL; /* counter for diagonal lines */
} else {
if (counterL > 0 && counterL < size) histL[counterL] += 2;
counterL = 0;
}
}
if (counterL > 0 && counterL < size) { histL[counterL] += 2; counterL = 0; }
if (counterL > 0 && counterL == size) { histL[counterL] += 1; counterL = 0; }
}

 Junior
 Posts: 2
 Joined: Fri Nov 23, 2012 04:13
 Affiliation (Univ., Inst., Dept.): Universidade Federal Fluminense
 Location: Brazil  Rio de Janeiro
 Research field: Physics  complex systems
Re: Identifying structures on RPs
Thanks Nobert,
now I understand, it is very simple.
Regards.
now I understand, it is very simple.
Regards.