Progress report

As I haven't had any significant roadblock or breakthroughs this week I wanted to give a little progress report on my work.
1. Added functionality
I have managed to add the following functions:

• mutual
• spectrum
• lazy
• delay
• pca

Along with their documentation, tests and a demo (for lazy). I was really happy that once I had produced some examples of how I want to port these functions the process of porting each one accelerated rapidly. 

I am especially excited about the fact that I have now henon, delay, an equivalent of addnoise and project available as this allowed me to create a nice noise reduction demo for project (and for lazy, but the one for project is more impressive). Fig.1 sums those efforts up.

Fig. 1 Noisy data and data cleaned up by project.

2. Functions found to be non-equivalent

I also spent a lot of my time (almost a week) researching which programs from TISEAN have a GNU Octave equivalent. Apart from my positive identifications, most of which I discussed in previous posts, I have made some negative ones. I found that both extrema and polynom have no GNU Octave equivalent. 

There was a suggestion made that extrema might be similar to findpeaks from signal. The only problem is that findpeaks searches (and returns) all peaks, whereas extrema returns either minimums or maximums. It might be easier to implement it in Octave than to port, but this decision has not been made yet.

The latter program polynom was compared to detrend, polyfit and wpolyfit. The results were disappointing. All of the GNU Octave functions attempt to fit a polynomial onto the data, whereas polynom tries to make a "polynomial ansatz" for the data. The results are vastly different as can be seen on Fig. 2.

Fig. 2 Comparison of original data (green), polyfit fit (red), and polynom prediction (blue).

Both programs were run to try to use a 4th order polynomial.