The following is distilled from the Projects page for the benefit of potential Summer of Code students. Although students are welcome to attempt any of the projects in that page or any of their own choosing, here we offer some suggestions on what good student projects might be.
Octave is mostly written in (sadly, mostly undocumented) C++ and its own scripting language (m-scripts), which includes (or should include) most of the Matlab language as a subset. We generally prefer a different Octave house style to the usual Matlab style for m-scripts, but it's primarily a superficial stylistic difference. Additionally, there are bits and pieces of Fortran, Perl, C, awk, and Unix shell scripts here and there. In addition to being familiar with C++ and/or Octave or Matlab's scripting languages, you should probably be familiar or learn about Octave's infrastructure:
- The GNU build system is used to build Octave. While you generally don't need to understand too much unless you actually want to change how Octave is built, you should be able to understand enough to get a general idea of how to build Octave. If you've ever done a configure && make && make install series of commands, you have already used the GNU build system.
- Mercurial (abbreviated hg) is the distributed version control system (DVCS) we use for managing our source code. You should have some basic understanding of how a DVCS works, but hg is pretty easy to pick up, especially if you already know a VCS like git or svn.
- You should also read the same contributing guidelines we have for everyone.
- We primarily use mailing lists for communication. You should follow basic mailing list etiquette. For us, this mostly means "do not top post".
- We also have an IRC channel. The atmosphere is more relaxed, and we may talk about things that are not at all related to Octave.
- Octave-Forge is a project closely related to Octave where packages reside. They are somewhat analogous to Matlab's toolboxes.
- In addition, you probably should know some mathematics, engineering, or experimental science or something of the sort. If you've used Matlab before, you probably have already been exposed to the kinds of problems that Octave is used for.
The following projects are broadly grouped by category and probable skills required to tackle each. Remember to check Projects for more ideas if none of these suit you, and your own ideas are always welcome.
These projects involve implementing certain mathematical functions in Octave.
Required skills: You should understand quite a bit of mathematics. Words like "eigenvalue", "analytic", and "Taylor series" shouldn't scare you at all. There is probably little C++ experience required, and probably many of these problems can be solved with m-scripts.
Difficulty: Mid-to-hard depending how much mathematics you know and how well you can read numerical analysis journal articles.
Potential mentor: Carlo de Falco, Nir Krakauer, Fotios Kasolis, Luis Gustavo Lira
Incomplete sparse factorizations ichol, ilu
Implement incomplete Cholesky and LU factorization for sparse matrices. These functions are available in Matlab as cholinc/ichol and luinc/ilu. Incomplete factorizations are useful as preconditioners for iterative solvers such as gmres and gmres or pcg. The classic book Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods has a chapter describing the ILU algorithm in detail, though the algorithm described there should be adapted to Octave's internal Sparse Matrix file format which is CCS rather than CRS. The implementation of ILU in Octave has been recently discussed in the maintainers list and initial implementations were posted in this thread. In another thread it was suggested to implement the ILU by interfacing Octave to ITSOL
Improve logm, sqrtm, funm
Generalised eigenvalue problem
Certain calling forms of the eig function are missing. The problem is to understand what those missing forms are and implement them.
Various sparse matrix improvements
The implementation of sparse matrices in Octave needs several improvements. Any of these would be good. The paper by Bateman & Adler is good reading for understanding the sparse matrix implementation.
Implement solver for initial-boundary value problems for parabolic-elliptic PDEs in 1D
The project will deliver a solver for initial-boundary value problems for parabolic-elliptic PDEs in 1D similar to Matlab's function pdepe. A good starting point is the method of lines for which you can find more details here and here, whereas an example implementation can be found here. In addition, this page provides some useful material.
Octave is currently working on a new native GUI. It is written in Qt, but it is still not ready for production. There are various ways in which it could be improved.
Required skills: C++ and Qt. Whatever tools you want to use to write Qt code are fine, but Qt Creator is a popular choice nowadays.
Difficulty: Mostly medium, depending if you've had Qt or GUI development experience before.
Potential mentor: Jordi Gutiérrez Hermoso, Michael Goffioul
Finish the Octave GUI
The GUI is currently on its own branch in hg. It is not stable enough and its design is still in flux. It is in a very alpha stage and needs to be turned into a real usable product. At the moment, it consists of the basic building blocks (terminal window, editor, variable browser, history, file browser) that are put together into a main interface. The GUI uses the Qt library. Among the things to improve are:
- define and implement a flexible docking system allowing to place any subwindow at any location
- improve integration with octave: variable browser/editor, debugger, profiler...
- define and implement an option/preferences dialog
- improve additional components like the embedded IRC client or the documentation browser
Integrate the GUI with the Octave build system
The current GUI build system is independent of Octave. First one builds and installs Octave, and then the GUI. The goal of this project is to integrate the GUI and make it all build together. Good understanding of both the GNU build system and Qt's (qmake and the meta-object compiler) will be necessary here.
Implement a Qt widget for manipulating plots
Octave has had for some time a native OpenGL plotter. The plotter requires some user interaction for manipulating the plots, and it's been using fltk for quite some time. We want to replace this with Qt, so it fits better with the overall GUI look-and-feel and is easier to extend in the future.
QtHandles is a current work in progress integrating the octave OpenGL renderer plus good support for GUI elements (uicontrol, uimenu, uitoolbar...). This project may initially consists of integrating the existing QtHandles code base into Octave. Then if time permits, further improvements can be made to QtHandles.
Create a better (G)UI for the profiler
During GSoC 2011, Daniel Kraft successfully implemented a profiler for Octave. It needs a better interface and a way to generate reports. This may be done with Qt, but not necessarily, and HTML reports might also be good.
Create a graphical design tool for tuning closed loop control system (control pkg)
When tuning a SISO feedback system it is very helpful to be able to grab a pole or a zero and move them by dragging them with the mouse. As they are moving the software must update all the plotted lines. There should be the ability to display various graphs rlocuse, bode, step, impulse etc. and have them all change dynamically as the mouse is moving. The parameters of the compensator must be displayed and updated. Potential mentor: Doug Stewart
Octave has a new native OpenGL plotter (currently via fltk, but we want to move away from that). There are several possible projects involved with it. Michael Goffioul has expressed interest in mentoring these projects.
Required skills: C++ and OpenGL. General understanding of computer graphics.
Difficulty: Medium, depending on your previous understanding of the topic.
Potential mentor: Michael Goffioul
Implement transparency and lighting in OpenGL backend(s). A basic implementation was available in JHandles. This needs to be ported/re-implement/re-engineered/optimized in the C++ OpenGL renderer of Octave.
Object selection in OpenGL renderer
This project is about the implementation of a selection method of graphics elements within the OpenGL renderer 
Besides the original gnuplot backend, Octave also contains an OpenGL-based renderer for advanced and more powerful 3D plots. However, OpenGL is not perfectly suited for 2D-only plots where other methods could result in better graphics. The purpose of this project is to implement an alternate graphics renderer for 2D only plots (although 3D is definitely not the focus, extending the new graphics renderer to support basic 3D features should also be taken into account). There is not fix constaints on the toolkit/library to use, but natural candidates are:
- Qt: the GUI is currently written in Qt and work is also in progress to provide a Qt/OpenGL based backend 
- Cairo: this library is widely used and known to provides high-quality graphics with support for PS/PDF/SVG output.
Text objects in plots (like titles, labels, texts...) in the OpenGL renderer only support plain text mode without any formatting possibility. Support for TeX and/or LaTeX formatting needs to be added.
The TeX formatting support actually only consists of a very limited subset of the TeX language. This can be implemented directly in C++ into Octave by extending the existing text engine, avoiding to add a dependency on a full TeX system.
On the other hand, the LaTeX formatting support is expected to provide full LaTeX capabilities. This will require to use an external LaTeX system to produce text graphics in some format (to be specified) that is then integrated into Octave plots.
The interpreter is written in C++, undocumented. There are many possible projects associated with it.
Required skills: Very good C and C++ knowledge, possibly also understanding of GNU bison and flex. Understanding how compilers and interpreters are made plus being able to understand how to use a profiler and a debugger will probably be essential skills.
Difficulty: Mid hard to very hard. Some of the biggest problems will probably be the interpreter.
Potential mentors: John W. Eaton, Jordi Gutiérrez Hermoso
Implement (or improve?) JIT compiling
Octave's interpreter is very slow on loops. Implementing JIT compiling would dramatically speed up execution of these loops. This is a very big project, but a dedicated student might make a good attempt of doing this over a summer. There may be some work already in place by the time the summer comes along. The idea is to probably use LLVM to aid with the JIT compilation.
Improve memory management
From profiling the interpreter, it appears that a lot of time is spending allocating and deallocating memory. A better memory management algorithm might provide some improvement.
Implement classdef classes
Matlab has two kinds of classes: old style @classes and new style classdef. Octave has only implemented the old style. Although the lexer and parser have been updated to recognise the syntax for the new style classdef declarations, they currently do nothing with it. A successful project would design and implement the necessary functionality for these classes. This project is somewhat simpler than others in the interpreter group.
There are several projects closely related to Octave but not exactly core Octave that could be worked on. They are mostly infrastructure around Octave, stuff that would help a lot.
Required skills: Various. See below.
Difficulty: Various. See below.
Potential mentor: Jordi Gutiérrez Hermoso, Carlo de Falco
Finish the Agora website
In response to this, a website started to form, Agora Octave.
This should be relatively easy webdev in Python using Django.
Give maintenance to the Emacs octave mode
Improve binary packaging
We would like to be able to easily generate binary packages for Windows and Mac OS X. Right now, it's difficult and tedious to do so. Any way to help us do this in a faster way would be appreciated. Required knowledge is understanding how building binaries in Windows and Mac OS X works. Medium difficulty.
Installation of packages
We would like to enhance the management of Octave-forge packages from within Octave environment. Currently there is a working (but rather monolithic) function that is used to do the job. The work would be to improve the way Octave interacts with the package server. Since the functionality is already sketched by the current function, the most important skill is software design.
Minimum requirements: Ability to read and write Octave code. Minimal FTP/HTTP knowledge.
Rewrite symbolic package
Octave's current symbolic package for symbolic computation is outdated, fragile and limited in its capabilities. The new symbolic package should offer better Matlab compatibility, for example handling of symbolic matrices. Like the current symbolic package, the new package could use the proven GiNaC library for symbolic computations.
The work would be to integrate GiNaC by using Octave's objects and classes. This can be done in C++ in a way similar to Michele Martone's new sparsersb package.
Required skills: C++. Ability to understand Octave and GiNaC API documentation.
Potential mentor: Lukas Reichlin
Octave currently provides file I/O and sockets for communicating with the outside world. Also, the instrument control package provides basic interfaces for RS232, I2C and the Parallel port. The project would extend the current communication interfaces in octave, allowing octave to directly communicate with measurement systems, data acquisition systems, sensors, robotic systems and the like.
Potential interfaces to support could, for example, be GPIB, USB HID, USBTMC, CAN, LIN, SPI. One initial task of the student would be to select a subset of these standards to support, taking, for example, existing drivers into account.
Required skills: C++, system programming knowledge, knowledge of Octave's current handling of file descriptors.
Difficulty: Mostly medium, depending depending on existing driver support and experience with the protocols
Potential mentors: Michael Godfrey(?), Andrius Sutas(?), Juan Pablo carbajal