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→Tutorials: added section: testing for nonlinearity
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=== Dimensions and Entropies === | === Dimensions and Entropies === | ||
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); | |||
# 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}); | |||
hold off | |||
xlabel ("Epsilon") | |||
ylabel ("Correlation sums") | |||
title ("c2"); | |||
# Plot correlation entropy | |||
subplot (2,3,4) | |||
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>}} | |||
[[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}}. | |||
=== 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"> | ||