Agreed, Python with NumPy is definitely a key player in this space, probably more significant these days than Matlab. Don't forget Octave which continues to hold it's place as a Open Matlab compatible(ish) option. Whilst I'm a fan of R for experimentation and prototyping it is often let down by poor performance, particularly on matrix calculations. R's forte is really in providing reference implementations of an amazing array of statistical methods, often by the author of the technique.
One of advantages of Julia touted by the authors is that much of the Julia system is written in the Julia language making it easy for users to understand many of the algorithms and contribute to the system. In practice I don't know how true that is (it seemed to spend a long time compiling C/C++ code when I last built it) but I can see the rationale.
One of advantages of Julia touted by the authors is that much of the Julia system is written in the Julia language making it easy for users to understand many of the algorithms and contribute to the system. In practice I don't know how true that is (it seemed to spend a long time compiling C/C++ code when I last built it) but I can see the rationale.