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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. | ||

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