Difference between revisions of "TISEAN package"

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m (→‎Noise Reduction: code bug)
(Started adding lzo_* example)
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* [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/tutorial/amplitude.dat amplitude.dat]
 
* [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.
 
Please download it as the tutorial will reference it.
=== Noise Reduction ===
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=== Nonlinear Prediction ===
This tutorial show different methods of the '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.
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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/>
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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">
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# Load data
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load amplitude.dat
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# Create different forecast error results
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steps = 200;
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res1  = lzo_test (amplitude, 'm', 2, 'd', 6, 's', steps);
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res2  = lzo_test (amplitude, 'm', 3, 'd', 6, 's', steps);
 +
res3  = lzo_test (amplitude, 'm', 4, 'd', 1, 's', steps);
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res4  = lzo_test (amplitude, 'm', 4, 'd', 6, 's', steps);
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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;',...
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      res4(:,1), res4(:,2), 'm;m = 4, d = 6;');
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</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">
 
{{Code|Creating a noisy henon map|<syntaxhighlight lang="octave" style="font-size:13px">
 
hen      = henon (10000);
 
hen      = henon (10000);

Revision as of 10:25, 1 June 2015

Porting TISEAN

This section will focus on demonstrating the capabilities of the TISEAN package. The previous information about the porting procedure has been moved here.


Tutorials

These tutorials are based on examples, tutorials and the articles located on the TISEAN website:
http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/.
This tutorial will utilize the following dataset:

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 here). For now this section will only demonstrate functions that are connected to the Simple Nonlinear Prediction section.
There are three functions in this section: lzo_test, lzo_gm and 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 (m,d) where chosen after the TISEAN documentation.

Code: Analyzing forecast errors for various parameters
# Load data
load amplitude.dat
# Create different forecast error results
steps = 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;');

It seems that the last pair {{{1}}} 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 here). It shows the use of simple nonlinear noise reduction (function lazy) and locally projective nonlinear noise reduction (function ghkss). To start let's create noisy data to work with.

Code: Creating a noisy henon map
hen       = henon (10000);
hen       = hen(:,1); # We only need the first column
hen_noisy = hen + std (hen) * 0.02 .* (-6 + sum (rand ([size(hen), 12]), 3));

This created a Henon map contaminated by 2% Gaussian noise à la TISEAN. In the tutorials and exercises on the TISEAN website this would be equivalent to calling makenoise -%2 on the Henon map.
Next we will reduce the noise using simple nonlinear noise reduction lazy.

Code: Simple nonlinear noise reduction
clean       = lazy (hen_noisy,7,-0.06,3);
# Create delay vectors for both the clean and noisy data
delay_clean = delay (clean);
delay_noisy = delay (hen_noisy);
# Plot both on one chart
plot (delay_noisy(:,1), delay_noisy(:,2), 'b.;Noisy Data;','markersize',3,...
      delay_clean(:,1), delay_clean(:,2), 'r.;Clean Data;','markersize',3)

On the chart created the red dots represent cleaned up data. It is much closer to the original than the noisy blue set.
Now we will do the same with ghkss.

Code: Locally projective nonlinear noise reduction
clean       = ghkss (hen,'m',7,'q',2,'r',0.05,'k',20,'i',2);

The rest of the code is the same as the code used in the lazy example.
Once both results are compared it is quite obvious that for this particular example ghkss is superior to lazy. The TISEAN documentation points out that this is not always the case.

External links