## 24 July 2012

### Coming to grips with the wavelet function

First off, OctConf was awesome! Meeting the other GSoC students and all the core developers was an awesome experience, and I hope I can go to more events in the future.

Now then. It is safe to say that the implementation of nurealwavelet() is in fact completely broken and may never have been meant to work. There's an infinite loop, there's an unused pointer, there's so many things wrong that I wonder how this article made it into print. On that note, I'm going to go over the entire function as it is represented in the paper here, and try to understand it. (In the following, the series is represented as a (t,ξ) series of complex values associated with a time series.)

$\bg_white \zeta _ { t, \omega } = \frac{ \sum _ { k \in K } w ( \sigma \omega ( t _ k - t ) ) e ^ { - i \omega ( t _ k - t ) } \xi _ k }{ \sum _ { k \in K } w ( \sigma \omega ( t _ k - t ) ) }$
From the context in the paper, it's clear that t has some import versus tk; unfortunately for me, how to use t is not at all clear. I am working from the assumption that t is supposed to be the centre of each window, and as such the proper implementation is to divide the range specified in the input by the number of intervals to determine the width of each interval (and thus the radius of said window being half again the width of the window), thus being able to apply the transform over the whole data set.

The problem that I've been avoiding so far is that the window changes as the frequency drops; a lower frequency requires a much larger window to define it, but this means the number of windows tested decreases, thus a matrix for storing results doesn't make sense, as it will become progressively more full of junk data/excess unused elements. I'm going to look for other wavelet transforms as they're performed with Octave to see what I can learn from others on how to implement this.

## 17 July 2012

### An exciting update on the fast functions

So, fastlscomplex and fastlsreal have had some problems. Lots of problems, in fact, and I wasn't really happy with my code. However, after rewriting most of fastlscomplex, I've got it correct on the first result, while further approximations appear to run afoul of compounding error. At the very least, however, this is far improved from the previous behaviour, and I'll work on getting fastlsreal rewritten.

## 10 July 2012

### Mid-session report

I really haven't updated recently. Then again, most of my recent work has been in fixing minor errors and adding documentation. So, as it stands, none of the tests I have written work if you call test() and the info strings (which I tried to make informative) also don't work. I have no clue why; Jordi thinks it's the negation field and I'm agreeing with him for now. I'm sure I'll find a way to fix it shortly. In the meantime, I'm reading the Introduction to Wavelets article and working on my presentation.

This will all be pretty cool, I think.