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== Porting TISEAN == | == Porting TISEAN == | ||
This section | This section which focuses on demonstrating how the package is to be ported and what is the current state of that process is located in [[TISEAN_package:Procedure]]. | ||
== Tutorials == | == Tutorials == | ||
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Once both results are compared it is quite obvious that for this particular example {{Codeline|ghkss}} is superior to {{Codeline|lazy}}. The TISEAN documentation points out that this is not always the case. | Once both results are compared it is quite obvious that for this particular example {{Codeline|ghkss}} is superior to {{Codeline|lazy}}. The TISEAN documentation points out that this is not always the case. | ||
[[File:tisean_nl_noisereduction_2.png|400px|center]] | [[File:tisean_nl_noisereduction_2.png|400px|center]] | ||
=== Lyapunov Exponents === | |||
Here I will demonstrate how to use the function {{Codeline|lyap_k}}. It estimates the maximal Lyapunov exponent from a time series (more information available from the TISEAN documentation located [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node27.html here]). In this tutorial we will estimate the maximal Lyapunov exponent for various embedding dimensions and then plot them. | |||
{{Code|Creating Lyapunov exponents|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
# Create time series | |||
in = sin((1:2500).'./360) + cos((1:2500).'./180); | |||
# Estimate Lyapunov exponents | |||
mmax_val = 20 | |||
lyap_exp = lyap_k (in, 'mmin',2,'mmax',mmax_val,'d',6,'s',400,'t',500); | |||
</syntaxhighlight>}} | |||
In this function the output ({{Codeline|lyap_exp}} is a {{Codeline|5 x 20}} struct array. We will only use one row for the plot. | |||
{{Code|Plotting Lyapunov exponents|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
cla reset | |||
hold on | |||
for j=2:mmax_val | |||
plot (lyap_exp(1,j-1).exp(:,1),lyap_exp(1,j-1).exp(:,2),'r'); | |||
endfor | |||
xlabel ("t [flow samples]"); | |||
ylabel ("S(eps, embed, t)"); | |||
hold off | |||
</syntaxhighlight>}} | |||
[[File:lyap_k.png|400px|center]] | |||
=== 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/node35.html#SECTION00090000000000000000 TISEAN documentation page]. The focus of this section will be the function {{Codeline|surrogates}}. It uses surrogate data to determine weather data is nonlinear. Let us first create the input data which will be a stationary Gaussian linear stochastic process. It is measured by {{Codeline|s(xn) = xn^3}}. We then run it through {{Codeline|surrogates}} and plot the data. | |||
{{Code|Creating data from Gaussian process|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
# Create Gaussian process data | |||
g = zeros (2000,1); | |||
for i = 2:2000 | |||
g(i) = 0.7 * g(i-1) + (-6 + sum (rand ([size(1), 12]), 3)); | |||
endfor | |||
# Create a measurement of it | |||
spike = g.^3; | |||
# Create the surrogate | |||
sur = surrogates (spike); | |||
# Plot the data | |||
subplot (2,1,1) | |||
plot (spike,'g'); | |||
title ("spike") | |||
subplot (2,1,2) | |||
plot (sur,'b'); | |||
title ("surrogate") | |||
</syntaxhighlight>}} | |||
[[File:surrogate_tutorial.png|400px|center]] | |||
It is crucial that the length of the input to surrogates is factorizable by only 2,3 and 5. Therefore, if it is not the excess of data is truncated accordingly. Padding with zeros is not allowed. To solve this problem one can use {{Codeline|endtoend}}, and choose the best subset of the input data to be used to generate a surrogate. | |||
[[Category:Octave-Forge]] | [[Category:Octave-Forge]] |
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