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=== Testing for Nonlinearity === | === Testing for Nonlinearity === | ||
This section is discussed on the [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/ | 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| | {{Code|Calculation correlation sum, dimension and entropy|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
# Create | # Create maps | ||
hen = henon (10000); | |||
# Calculate the correlation sum, dimension and entropy | |||
vals = d2 (hen, 'd', 1, 'm', 5, 't',50); | |||
# Plot correlation sum | |||
subplot (2,3,1) | |||
do_plot_corr = @(x) loglog (x{1}(:,1),x{1}(:,2),'b'); | |||
hold on | |||
arrayfun (do_plot_corr, {vals.c2}); | |||
# Plot | hold off | ||
subplot (2,1,1) | xlabel ("Epsilon") | ||
ylabel ("Correlation sums") | |||
title (" | title ("c2"); | ||
subplot (2, | # Plot correlation entropy | ||
subplot (2,3,4) | |||
title (" | do_plot_entrop = @(x) semilogx (x{1}(:,1),x{1}(:,2),'g'); | ||
hold on | |||
arrayfun (do_plot_entrop, {vals.h2}); | |||
hold off | |||
xlabel ("Epsilon") | |||
ylabel ("Correlation entropies"); | |||
title ("h2") | |||
# Plot correlation dimension | |||
subplot (2,3,[2 3 5 6]) | |||
do_plot_slope = @(x) semilogx (x{1}(:,1),x{1}(:,2),'r'); | |||
hold on | |||
arrayfun (do_plot_slope, {vals.d2}); | |||
hold off | |||
xlabel ("Epsilon") | |||
ylabel ("Local slopes") | |||
title ("d2"); | |||
</syntaxhighlight>}} | </syntaxhighlight>}} | ||
[[File:d2_out.png|400px|center]] | |||
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). | |||
{{Code|Smooth output of d2|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
# Smooth d2 output | |||
figure 2 | |||
smooth = av_d2 (vals,'a',2); | |||
# Plot the smoothed output | |||
do_plot_slope = @(x) semilogx (x{1}(:,1),x{1}(:,2),'b'); | |||
hold on | |||
arrayfun (do_plot_slope, {smooth.d2}); | |||
hold off | |||
xlabel ("Epsilon") | |||
ylabel ("Local slopes") | |||
title ("Smooth"); | |||
</syntaxhighlight>}} | |||
[[File:tisean_av_d2_out.png|400px|center]] | |||
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}}. | |||
[[ | [[Category:Octave-Forge]] | ||
== External links == | == External links == | ||
* [https://bitbucket.org/josiah425/tisean Bitbucket repository ] where the porting is taking place. | * [https://bitbucket.org/josiah425/tisean Bitbucket repository ] where the porting is taking place. | ||
* [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/ TISEAN package website] where the package is described along with references to literature, tutorials and manuals. | * [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/ TISEAN package website] where the package is described along with references to literature, tutorials and manuals. | ||