I am aware that C/C++ is a lower-level language and generates relatively optimized machine code when we compare with any other high-level language. But I guess there is pretty much more than that, which is also evident from the practice.
When I do simple calculations like montecarlo averaging of a Gaussian sample collection or so, I see there is not much of a difference between a C++ implementation or MATLAB implementation, sometimes in fact MATLAB performs a bit better in time.
When I move on to larger scale simulations with thousands of lines of code, slowly the real picture shows up. C++ simulations show superior performance like 100x better in time complexity than an equivalent MATLAB implementation.
The code in C++ most of the times, is pretty much serial and no hi-fi optimization is done explicitly. Whereas, as per my awareness, MATLAB inherently does a lot of optimization. This shows up for example when I try to generate a huge chunk of random samples, where as the equivalent in C++ using some library like IT++/GSL/Boost performs relatively slower (the algorithm used is the same namely mt19937).
My question is simply to know if there is a simpler tradeoff between MATLAB/C++ in performance. Is it just like what people say, "Whenever you can, C/C++ is the better"(The frequently experienced)?. In a different perspective, "What is MATLAB good for, other than comfort?"
By the way, I don't see coding efficiency parameter being significant here, thinking of the same programmer in both cases. And also, I think the other alternatives like python,R are not relevant here. But dependence on the specific libraries we use should be interesting.
[I am a phd student in Coding Theory in communication systems. I do simulations using matlab/C++ all the time, and have reasonable experience of coding few 10K's of lines in both cases]