The first day and my repository

Yesterday I handed in the last exam for the semester(!) and today I started to work on the project full time. I begun by setting up a repository for my code. At the moment I have only cloned the interval package, I'm still to make my own changes to it.

I started to read the constructor for intervals to see how it works. While doing that I realized that there is much less to do than I thought. The constructor can actually handle creating intervals from numerical arrays of any dimension. The function displaying the interval can only handle up to two dimension but if you look at the internal state it actually has more dimensions. It is not perfect though, it does not work for decorated intervals and it cannot handle strings and cells as input. But still, it makes it much easier for me.

I will continue to work and hopefully I have actually committed something by the end of the week. Next week I will be away but after that I will code for the rest of the summer.

Timeline

This post will be about specifying a timeline for my work this summer. As I mentioned in the introductory post the work will be about implementing support for higher dimensional arrays in the interval package. To begin with I have divided the work into 5 different parts:

1. Construction and Printing

This part will be about implementing functions for creating and printing arrays. It will mainly consist of modifying the standard constructor and all the different functions used for printing intervals so they can handle higher dimensional arrays.

2. Vectorized Functions

Here I will work on generalizing all functions supporting vectorization to also support arrays of higher dimensions.

3. Folding Functions

Here I will work on generalizing all functions implementing some sort of folding to support higher dimensions. By folding I mean taking a multidimensional array as input and returning an array of lower dimension. Examples of these functions are $sum$, $prod$ and $dot$.

4. Plotting

I'm not sure what support Octave has for plotting higher dimensional arrays, but if there are some functions which could also be useful for intervals I will try to implement them here.

5. Documentation

I'll write the documentation alongside the rest of the work. In the end I will try to add some usage examples and integrate it better with the standard documentation.

So these are the parts in which I have divided my work in and the timeline will be

• Phase 1 (30/5 - 30/6)
• Week 1: Setting up
• Week 2-3: Construction and Printing
• Week 4: Vectorized Functions
• Phase 2 (3/7 - 28/7)
• Week 5: Continue on Vectorized Functions 
• Week 6-7: Folding Functions
• Week 8: Plotting
• Phase 3 (31/7 - 25/8)
• Week 9: Continue on Plotting
• Week 10-11: Documentation
• Week 12: Finishing up!

My first week will be rather short since I have an exam due in the middle of the week. After that I will also be away for a week not working on the project, I have no counted that week in the timeline above.

Introduction

Hi! I'm Joel Dahne and I will be using this blog to share the progress of my work for Google Summer of Code 2017 under GNU Octave where I will be working on improving the interval package.

About me

Currently I'm a master student in mathematics at Uppsala University, Sweden, I'm just about to complete my first year and have one more to go. I first encountered interval numerics with my bachelor thesis, during which I tried to generalize the method described in this paper to higher dimensions. The code from the project is available on GitHub, https://github.com/Urathai/generateZeros. Working on that project ignited my interest for interval numerics and I want to work to increase its availability to the common user.

The project

In short my project is about adding support for N-dimensional arrays in the interval package. At the moment the package only has support for up to 2-dimensional arrays. Most of the time this is enough but sometimes it is limiting. The goal is to have the syntax identical to the one for normal arrays. Switching from floats to intervals should be as easy as adding $infsup$ in front of the variable.

During my time preparing I have also noticed that some of the folding functions (e.g. $sum$, $prod$ and $dot$) handle some edge cases differently than the standard implementation. Hopefully this can be resolved at the same time.

This blog

During my project I will try to update this blog with my current progress. It's my first time writing a blog so we will see how it goes. The next step for me is to create more detailed plan of how I should structure my work during the summer, this will most likely be the subject of my next post.