TISEAN package: Difference between revisions

This section is discussed on the [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node29.html#SECTION00080000000000000000 TISEAN documentation page]. One of the functions discussed is {{Codeline|d2}}. It is used to estimate the correlation sum, correlation dimension and correlation entropy of a time series. The time series used here will be the Henon map.

{{Code|Calculation correlation sum, dimension and entropy|<syntaxhighlight lang="octave" style="font-size:13px">

# Create maps

hen      = henon (10000);

vals = d2 (hen, 'd', 1, 'm', 5, 't',50);

subplot (2,3,1)

do_plot_corr = @(x) loglog (x{1}(:,1),x{1}(:,2),'b');

arrayfun (do_plot_corr, {vals.c2});

# Plot correlation entropy

do_plot_entrop  = @(x) semilogx (x{1}(:,1),x{1}(:,2),'g');

arrayfun (do_plot_entrop, {vals.h2});

xlabel ("Epsilon")

ylabel ("Correlation entropies");

# Plot correlation dimension

subplot (2,3,[2 3 5 6])

do_plot_slope = @(x) semilogx (x{1}(:,1),x{1}(:,2),'r');

title ("d2");

The output of {{Codeline|d2}} can be further processed using the following functions: {{Codeline|av_d2}}, {{Codeline|c2t}}, {{Codeline|c2g}}. This tutorial will show how to use {{Codeline|av_d2}} which smooths the output of {{Codeline|d2}} (usually used to smooth the "{{Codeline|d2}}" field of the output).

figure 2

smooth = av_d2 (vals,'a',2);

do_plot_slope = @(x) semilogx (x{1}(:,1),x{1}(:,2),'b');

title ("Smooth");

Optionally the line "{{Codeline|figure 2}}" can be omitted, which will cause the smoothed version to be superimposed on the "raw" version that came straight from {{Codeline|d2}}.