In short, both GNU Octave and FreeMat are open-source alternatives to MATLAB. However, Octave is more mature and has wider community support.
I also found this interesting article that compares MATLAB, Octave, FreeMat and SciLab. It does point out a few issues against FreeMat:
- It doesn’t support some functions (such as
kron
andpcg
). - It has limited 3-D graphics capabilities (e.g. no support for the
mesh
function). - It is also lacking in the ODE department, for not having a state-of-the-art solver.
Essentially, this article concludes that Octave is indeed the most compatible with MATLAB at present.
Now, if you’re searching for a good GUI/IDE, try one of these.