This section will focus on demonstrating the capabilities of the TISEAN package. The previous information about the porting procedure has been moved here.
These tutorials are based on examples, tutorials and the articles located on the TISEAN website:
This tutorial will utilize the following dataset:
Please download it as the tutorial will reference it.
This tutorial show different methods of the '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
|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
|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
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.