GNU Octave uses the Matlab language, though not all the libraries that are available for Matlab are avaialble for GNU Octave. This does not prevent you from coding these functions up yourself. The GNU Octave team has a reporting method that allows you to report if a function does not work the same as it does in Matlab.
GNU Octave is also uses the interpreted method. Both Python and C# are interpreted, but I am not sure about R. I know of it, but I have not used it.
One of these days I will go and play with Python. It seems that it is popular. I have not used R, but like you said, it is geared towards stats. The one thing that I really like about the Matlab language is the fact that it handles the input of vectors and matricies so well. It is just as a TI calculator handles it. One of these days I may also try F#. That seems like it could be a nice language for doing numerical analysis. So much to learn, so little time!
I'm not ready to use F# in production (partly because I don't think most other programmers would be able to maintain the code), but after skimming Programming F# I can say it looks groovy. It's also featured in Real World Functional Programming (along with C#). It's real mind expander (in a good way) for most programmers (including myself, although I've been using some functional techniques for years).
Yeah, I almost launched into learning F#, but I will wait for a while. It does look really nice, and the fact that it can be done Visual Studio is also a plus in my book. I really like the Visual Studio IDE. Eclipse is also nice, but I am not the biggest fan of Netbeans. It just has some things that make me scratch my head from time to time. My only exposure to Netbeans has been with MPLAB X, and it was a great step up in features compared to MPLAB 8, but then I started to learn the ARM Cortex M series chips from various vendors and they are all using Eclipse of one form or another. I like it much more over Netbeans. As for trying to learn C#, I have also really also enjoyed Visual Studio.
@Aeroengineer: "One of these days I will go and play with Python. It seems that it is popular"
I started to learn Python in January and this is a very powerful mathematics tool when used in combination with NumPy, SciPy and Matplotlib packages. You can work out filter coefficients and responses in a very similar way to that of Matlab/Octave -- there are a lot of libraries included on SciPy!!
Python is becoming very popular in scientific applications, and a growing number of universities and research centers are using it -- the great advantage of Python for scientific programming is its focus on code readability.
But for sure, a lot of students knows to program in Matlab language, so Octave has been a great alternative for those --like me-- who love Open Source!!
In the good old days of Scope Junction, Michael did a series of blogs evaluating the different options. As we all know the old content is not available (grumble and mutter), but if you contact him (via EDN's Design Ideas I guess) he should still have access to those blogs.
Do you happen to know the title of the post, I may be able to go to the internet wayback machine and pull it up. I will be honest that the main reason that I have gone after GNU Octave is because I already have some familiarity in the language and I needed to get something done without having to learn another language. The specific version of GNU Octave I mentioned is a particularly nice version. It is kept up to date as well as improved rather constantly.