Differences between Octave and MATLAB?

MATLAB is, first and foremost, a commercial offering. Therefore, everything in MATLAB pretty much works out of the box. All the core functionality is solid, and if you're working on a special project then MATLAB probably has an add-on they can sell you that adds a lot of additional domain-specific .m files for you. It isn't cheap, but it works and it will get the job done without complaint.

Octave always shows its open-source, information-wants-to-be-free roots. It's free, and it will remind you that it's free at every opportunity. It's developed by volunteers who hate Windows with a passion. Therefore Octave runs on Windows grudgingly. It's quite surprising that as many MATLAB features exist as they do.

But here's the rub. Anytime you try to do something more than trivially complex, Octave suddenly breaks in subtle and hard-to-understand ways. Oops -- the terminal driver had an overflow somewhere deep in the OpenGL layer. You can't print. Oops -- the figure plots do strange things with their fonts. Good luck figuring out why. Oops -- there's some hidden dependency between Octave and some other obscure bit of free software, so it won't compile. Good luck figuring out which it is.

And the Octave response is hey! It's free software! You have all the source code, and you can fix all those bugs yourself! Maybe if I had infinite time and resources on my hands, I could spend all my time fixing bugs in free software, but I personally don't. If I worked in academia, I might.

So at the core, the issue of whether to choose MATLAB or Octave comes down to one question. Interestingly, that question is always the same, when choosing between commercial vs. free software variants.

And the question is:

Do you have more money than time?

Rather than provide you with a complete list of differences, I'll give you my view on the matter.

If you read carefully the wiki page you provide, you'll often see sentences like "Octave supports both, while MATLAB requires the first" etc. This shows that Octave's developers try to make Octave syntax "superior" to MATLAB's.

This attitude makes Octave lose its purpose completely. The idea behind Octave is (or has become, I should say, see comments below) to have an open source alternative to run m-code. If it tries to be "better", it thus tries to be different, which is not in line with the reasons most people use it for. In my experience, running stuff developed in MATLAB doesn't ever work in one go, except for the really simple, really short stuff -- For any sizable function, I always have to translate a lot of stuff before it works in Octave, if not re-write it from scratch. How this is better, I really don't see...

Also, if you learn Octave, there's a lot of syntax allowed in Octave that's not allowed in MATLAB. Meaning -- code written in Octave often does not work in MATLAB without numerous conversions. It's also not compatible the other way around!

I could go on: The MathWorks has many toolboxes for MATLAB, there's Simulink and its related products for which there really is no equivalent in Octave (yes, you'd have to pay for all that. But often your employer/school does that anyway, and well, it at least exists), proven compliance with several industry standards, testing tools, validation tools, requirement management systems, report generation, a much larger community & user base, etc., etc., etc. MATLAB is only a small part of something much larger. Octave is...just Octave.

So, my advice:

• Find out if your school will pay for MATLAB. Often they will.
• If they don't, and if you can scrape together the money, buy MATLAB and learn to use it properly. In the long run it's the better decision.
• If you really can't get the money -- use Octave, but learn MATLAB's syntax and stay away from Octave-only syntax. (see note)

Why this last point? Because in the sciences, there are often large code bases entirely written in MATLAB. There are professors, engineers, students, professional coders, lots and lots of people who know all the intricate gory details of MATLAB, and not so much of Octave.

If you get a new job, and everyone in your new office speaks Spanish, it's kind of cocky to demand of everyone that they start speaking English from then on, simply because you don't speak/like Spanish. Same with MATLAB and Octave.

Note: Octave can be run in "traditional mode" (by including the --traditional flag when starting Octave) which makes it give an error when certain Octave-only syntax is used.

A more complete link to the list of differences is on the Octave's FAQ. In theory, all code that runs in Matlab should run in Octave and Octave developers treat incompatibility with Matlab as bugs. So the answer to your first question is yes in theory. Of course, all software has bugs, neither Octave or Matlab (yes, Matlab too) are safe from them. You can report them and someone will try to fix them

Octave also has extra features, most of them are extra syntax which in my opinion make the code more readable and more sense, specially if you are used to other programming languages.

But there's more to Octave than just the monetary cost. Octave is free also in the sense of freedom, it's libre, but I don't think this is the place to rant about software freedom.

I do image processing in Octave only and find that the image package suits my needs. I don't know, however, what will be yours. So my answer to if it's worth the cost is no, but certainly others will disagree.