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TISEAN package

1,894 bytes added, 11:25, 1 June 2015
Started adding lzo_* example
* [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/tutorial/amplitude.dat amplitude.dat]
Please download it as the tutorial will reference it.
=== Nonlinear Prediction ===In this section we will demonstrate some functions from the 'Nonlinear Prediction' chapter of the TISEAN documentation (located [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node16.html#SECTION00050000000000000000 here]). For now this section will only demonstrate functions that are connected to the [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node18.html#SECTION00052000000000000000 Simple Nonlinear Prediction] section. <br/>There are three functions in this section: {{Codeline|lzo_test}}, {{Codeline|lzo_gm}} and {{Codeline|lzo_run}}. The first is used to estimate the forecast error for a set of chosen parameters, the second gives the some global information about the fit and the third produces predicted points. Let us start with the first one (before completing starting this example remember to download 'amplitude.dat' from above and start Octave in the directory that contains it). The pairs of parameters {{Codeline|(m,d)}} where chosen after the TISEAN documentation.{{Code|Analyzing forecast errors for various parameters|<syntaxhighlight lang="octave" style="font-size:13px"># Load dataload amplitude.dat# Create different forecast error resultssteps = 200;res1 = lzo_test (amplitude, 'm', 2, 'd', 6, 's', steps);res2 = lzo_test (amplitude, 'm', 3, 'd', 6, 's', steps);res3 = lzo_test (amplitude, 'm', 4, 'd', 1, 's', steps);res4 = lzo_test (amplitude, 'm', 4, 'd', 6, 's', steps);plot (res1(:,1), res1(:,2), 'r;m = 2, d = 6;', ... res2(:,1), res2(:,2), 'g;m = 3, d = 6;',... res3(:,1), res3(:,2), 'b;m = 4, d = 1;',... res4(:,1), res4(:,2), 'm;m = 4, d = 6;');</syntaxhighlight>}}It seems that the last pair {{Codeline|m = 4, d = 6}} is suitable. We will use it to determine the the best neighborhood to use when generating future points. === Nonlinear Noise Reduction ===This tutorial show different methods of the 'Nonlinear Noise Reduction' section of the TISEAN documentation (located [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node22.html#SECTION00060000000000000000 here]). It shows the use of simple nonlinear noise reduction (function {{Codeline|lazy}}) and locally projective nonlinear noise reduction (function {{Codeline|ghkss}}). To start let's create noisy data to work with.
{{Code|Creating a noisy henon map|<syntaxhighlight lang="octave" style="font-size:13px">
hen = henon (10000);
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