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→‎Tutorials: added section: testing for nonlinearity
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=== Dimensions and Entropies ===
 
=== Dimensions and Entropies ===
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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.
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{{Code|Calculation correlation sum, dimension and entropy|<syntaxhighlight lang="octave" style="font-size:13px">
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# Create maps
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hen      = henon (10000);
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# Calculate the correlation sum, dimension and entropy
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vals = d2 (hen, 'd', 1, 'm', 5, 't',50);
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# Plot correlation sum
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subplot (2,3,1)
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do_plot_corr  = @(x) loglog (x{1}(:,1),x{1}(:,2),'b');
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hold on
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arrayfun (do_plot_corr, {vals.c2});
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hold off
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xlabel ("Epsilon")
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ylabel ("Correlation sums")
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title ("c2");
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# Plot correlation entropy
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subplot (2,3,4)
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do_plot_entrop  = @(x) semilogx (x{1}(:,1),x{1}(:,2),'g');
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hold on
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arrayfun (do_plot_entrop, {vals.h2});
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hold off
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xlabel ("Epsilon")
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ylabel ("Correlation entropies");
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title ("h2")
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# Plot correlation dimension
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subplot (2,3,[2 3 5 6])
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do_plot_slope = @(x) semilogx (x{1}(:,1),x{1}(:,2),'r');
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hold on
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arrayfun (do_plot_slope, {vals.d2});
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hold off
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xlabel ("Epsilon")
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ylabel ("Local slopes")
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title ("d2");
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</syntaxhighlight>}}
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[[File:d2_out.png|400px|center]]
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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).
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{{Code|Smooth output of d2|<syntaxhighlight lang="octave" style="font-size:13px">
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# Smooth d2 output
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figure 2
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smooth = av_d2 (vals,'a',2);
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# Plot the smoothed output
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do_plot_slope = @(x) semilogx (x{1}(:,1),x{1}(:,2),'b');
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hold on
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arrayfun (do_plot_slope, {smooth.d2});
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hold off
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xlabel ("Epsilon")
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ylabel ("Local slopes")
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title ("Smooth");
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</syntaxhighlight>}}
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[[File:tisean_av_d2_out.png|400px|center]]
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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}}.
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=== Testing for Nonlinearity ===
 
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.
 
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">
 
{{Code|Calculation correlation sum, dimension and entropy|<syntaxhighlight lang="octave" style="font-size:13px">
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