# Changes

,  06:04, 14 August 2015
Line 140: Line 140:
=== 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">
156

edits