If my timeline would have been correct I would have just started to work on Folding Functions (or reductions as they are often called). Instead I have completed the work on them and also for functions regarding plotting. In addition I have started to work on the documentation for the package as well as checking everything an extra time.

In this blog post I will go through what I have done this week, what I think is left to do and a little bit about what I might do if I complete the work on N-dimensional arrays in good time.

## This Week

### The Dot Function

The $dot$-function was the last function left to implement support for N-dimensional arrays in. It is very similar to the $sum$-function so I already had an idea of how to do it. As with $sum$ I moved most of the handling of the vectorization from the m-files to the oct-file, the main reason being improved performance.The $dot$-functions for intervals is actually a bit different from the standard one. First of all it supports vectorization which the standard one does not

> dot ([1, 2, 3; 4, 5, 6], 5)

error: dot: size of X and Y must match

> dot (infsupdec ([1, 2, 3; 4, 5, 6], 5)

ans = 1x3 interval vector

[25]_com [35]_com [45]_com

It also treats empty arrays a little different, see bug #51333,

> dot ([], [])

ans = [](1x0)

> dot (infsupdec ([]), [])

ans = [0]_com

### Package Documentation

I have done the minimal required changes to the documentation. That is I moved support for N-dimensional arrays from Limitation to Features and added some simple examples on how to create N-dimensional arrays.### Searching for Misses

During the work I have tried to update the documentation for all functions to account for the support of N-dimensional arrays and I have also tried to update some of the comments for the code. But as always, especially when working with a lot of files, you miss things, both in the documentation and old comments.I did a quick grep for the words "matrix" and "matrices" since they are candidates for being changed to "array". Doing this I found 35 files where I missed things. It was mainly minor things, comments using the "matrix" which I now changed to "array", but also some documentation which I had forgotten to update.

## What is Left?

### Package Documentation - Examples

As mentioned above I have done the minimal required changes to the documentation. It would be very nice to add some more interesting example using N-dimensional arrays of intervals in a useful way. Ironically I have not been able to come up with an interesting example but I will continue to think about it. If you have an example that you think would be interesting and want to share, please let me know!### Coding Style

As I mentioned in one of the first blog posts, the coding style for the interval package was not following the standard for Octave. During my work I have adapted all files I have worked with to the coding standard for Octave. A lot of the files I have not needed to do any changes to, so they are still using the old style. It would probably be a good idea to update them as well.### Testing - ITF1788

The interval framwork libary developed by Oliver is used to test the correctness of many of the functions in the package. At the moment it tests evaluation of scalars but in principle it should be no problem to use it for testing vectorization or even broadcasting. Oliver has already started to work on this.## After N-dimensional arrays?

If I continue at this pace I will finish the work on N-dimensional arrays before the time of the project is over. Of course the things that are left might take longer than expected, they usually do, but there is a chance that I will have time left after everything is done. So what should I do then? There are more thing that can be done on the interval package, for example adding more examples to the documentation, however I think I would like to start working on a new package for Taylor arithmetics.Before GSoC I started to implement a proof of concept for Taylor arithmetics in Ocatve which can be found here. I would then start to work on implementing a proper version of it, where I would actually make use of N-dimensional interval arrays. If I want to create a package for this I would also need to learn a lot of other things, one of them being how to manage a package on octave forge.

At the moment I will try to finish my work on N-dimensional arrays. Then I can discuss it with Oliver and see what he thinks about it.

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