Line length distributions

Extract lengths of diagonal, vertical and horizontal line segments from a recurrence matrix.

rp_lineDist(
  RM,
  DLmin = 2,
  VLmin = 2,
  HLmin = 2,
  DLmax = length(Matrix::diag(RM)) - 1,
  VLmax = length(Matrix::diag(RM)) - 1,
  HLmax = length(Matrix::diag(RM)) - 1,
  d = NULL,
  theiler = NA,
  recurrenceTimes = FALSE,
  AUTO = NULL,
  chromatic = FALSE,
  matrices = FALSE
)

Arguments

RM

A distance matrix (set emRad = NA to estimate a radius), or a matrix of zeroes and ones

DLmin

Minimal diagonal line length (default = 2)

VLmin

Minimal vertical line length (default = 2)

HLmin

Minimal horizontal line length (default = 2)

DLmax

Maximal diagonal line length (default = length of diagonal -1)

VLmax

Maximal vertical line length (default = length of diagonal -1)

HLmax

Maximal horizontal line length (default = length of diagonal -1)

d

Vector of diagonals to be extracted from matrix RP before line length distributions are calculated. A one element vector will be interpreted as a windowsize, e.g., d = 50 will extract the diagonal band -50:50. A two element vector will be interpreted as a band, e.g. d = c(-50,100) will extract diagonals -50:100. If length(d) > 2, the numbers will be interpreted to refer to individual diagonals, d = c(-50,50,100) will extract diagonals -50,50,100. If length(d) is NULL, 1 or 2, the theiler window is applied before diagonals are extracted. The theiler window is ignored if length(d)>2, or if it is larger than the matrix or band indicated by parameter d. A warning will be given is a theiler window was already applied to the matrix.

theiler

Use a theiler window around the main diagonal (Line of Identity/Synchronisation) to remove auto-correlations at short time-lags:

• 0 will include the main diagonal in all RQA measure calculations.

• 1 will remove the main diagonal from all RQA measure calculations.

• NA (default), will check if the matrix is symmetrical , if so, it will remove the diagonal by setting theiler = 1 (Line of Identity, Auto-RQA), if it is not symmetrical (Line of Synchronisation, Cross-RQA) it will set theiler = 0.

• A value greater than 1 will remove that many diagonals around and including the diagonal from all RQA measure calculations. So theiler = 2 means exclude 2 diagonals around the main diagonal, including the main diagonal itself: [-1,0,1]. If theiler is a numeric vector of length(theiler) == 2 it is possible to exclude an asymmetrical window. The values are interpreted as end points in a sequence of diagonal ID's, e.g. theiler = c(-1,5) will exclude [-1,0,1,2,3,4,5]. If length(theiler) > 2, the values will be considered individual diagonal ID's, e.g. theiler = c(-3,-1,0,2,5), will exclude only those specific ID's. Also see the note.

recurrenceTimes

Relevant for Recurrence Time analysis: Return the distribution of 0 valued segments in nonzero diagonals/verticals/horizontals. This indicates the time between subsequent line structures.

AUTO

Auto-recurrence? (default = FALSE)

chromatic

Perform a chromatic RQA. This assumes the recurring values represent the labels of an unordered categorical variable (default = FALSE)

matrices

Return matrices? (default = FALSE)

Value

A list object with distributions of line lengths. If matrices = TRUE datafr are returned whose columns represent the nonzero diagonals, verticals, or, horizontals.

Details

Based on the Matlab function linedists by Stefan Schinkel, Copyright (C) 2009 Stefan Schinkel, University of Potsdam, http://www.agnld.uni-potsdam.de

References: S. Schinkel, N. Marwan, O. Dimigen & J. Kurths (2009): "Confidence Bounds of recurrence-based complexity measures Physics Letters A, 373(26), pp. 2245-2250

Copyright (C) 2009 Stefan Schinkel, University of Potsdam http://www.agnld.uni-potsdam.de

See also

Other Distance matrix operations (recurrence plot): bandReplace(), createCorridor(), mat_di2bi(), mat_di2ch(), mat_di2we(), mat_hamming(), rp(), rp_nzdiags(), rp_plot(), rp_size()

Author

Fred Hasselman